Exhibit 10.1

Execution Version

FIRST AMENDMENT

AMENDED AND RESTATED CREDIT AGREEMENT

dated as of September 25, 2012

among

Dune Energy, Inc.,

as Borrower,

Bank of Montreal,

as Administrative Agent,

CIT Capital Securities LLC,

as Syndication Agent,

and

The Guarantors and Lenders Party Hereto

BMO Capital Markets Corp.

Sole Lead Arranger and Sole Bookrunner

FIRST AMENDMENT TO

AMENDED AND RESTATED CREDIT AGREEMENT

THIS FIRST AMENDMENT TO AMENDED AND RESTATED CREDIT AGREEMENT (this “First Amendment”) dated as of September 25, 2012, is among DUNE ENERGY, INC., a Delaware corporation (the “Borrower”); certain of the lenders party to the Credit Agreement referred to below (collectively, the “Required Lenders”); and BANK OF MONTREAL, as administrative agent for the Lenders (in such capacity, together with its successors in such capacity, the “Administrative Agent”).

R E C I T A L S

A. The Borrower, the Administrative Agent and the Required Lenders are parties to that certain Amended and Restated Credit Agreement dated as of December 22, 2012 (the “Credit Agreement”), pursuant to which the Lenders have made certain credit available to and on behalf of the Borrower.

B. The Borrower has informed the Administrative Agent that Dune Operating Company, a Subsidiary of the Borrower, previously entered into an Emission Reduction Credits Purchase and Sale Agreement dated August 9, 2012 with Element Markets, LLC (the “ERC Agreement”) and the Borrower has requested, and the Administrative Agent and the Required Lenders have agreed, that the provisions of Section 9.12 of the Credit Agreement be waived with respect to the ERC Agreement.

C. The Borrower has requested and the Required Lenders have agreed to amend certain provisions of the Credit Agreement as set forth herein and affirm the current amount of the Borrowing Base.

D. Now, therefore, to induce the Administrative Agent and the Required Lenders to enter into this First Amendment and in consideration of the premises and the mutual covenants herein contained, for good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto agree as follows:

Section 1. Defined Terms. Each capitalized term used herein but not otherwise defined herein has the meaning given such term in the Credit Agreement, as amended by this First Amendment. Unless otherwise indicated, all section references in this First Amendment refer to sections of the Credit Agreement.

Section 2. Amendments to Credit Agreement.

2.1 Amendments to Section 1.02. Section 1.02 is hereby amended by deleting the defined term “Agreement” in its entirety and replacing it with the following:

“Agreement” means this Amended and Restated Credit Agreement, as amended by that certain First Amendment dated as of September 25, 2012, as the same may from time to time be amended, modified, supplemented or restated.

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2.2 Amendment to Section 8.01. Section 8.01 is hereby amended by inserting the following clause (p) after clause (o) in such Section:

“(p) Accounts Payable Aging Report. As soon as practicable and in any event within five (5) business days after the request of the Administrative Agent, an accounts payable aging report listing items which are customarily found in such reports for the most recently ended calendar month. This reporting requirement shall terminate on the last day of the first full fiscal quarter ending after January 1, 2013.”

2.3 Amendment to Section 9.01(a). Section 9.01(a) is hereby amended and restated in its entirety to read as follows:

(a) Ratio of Total Debt to EBITDAX. The Borrower will not, as of the last day of any fiscal quarter ending on or after December 31, 2011, permit its ratio of Total Debt as of such day to EBITDAX for the immediately preceding four fiscal quarters ending on such day to be greater than the ratio set forth below:

2.4 Amendment to Section 9.12. Section 9.12 is hereby amended by deleting the phrase “and” at the end of clause (e) thereof, replacing the period at the end of clause (f) thereof with the phrase “; and” and by inserting the following clause (g) at the end of such Section:

“(g) sales of emission reduction credits and other carbon sequestration or environmental credits.”

Section 3. Borrowing Base Redetermination. For the period from and including the Effective Date of this First Amendment to but excluding the next Redetermination Date, the amount of the Borrowing Base shall be $50,000,000. Notwithstanding the foregoing, the Borrowing Base may be subject to further adjustments from time to time pursuant to Section 2.07(e), Section 8.13(c) or Section 9.12(d).

Section 4. Waiver. Subject to the conditions precedent set forth in Section 5 of this First Amendment and the ratification and affirmation set forth in Section 6.2 of this First Amendment, the Administrative Agent and the Required Lenders herby waive the provisions of Section 9.12 with regard to the ERC Agreement.

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Section 5. Conditions Precedent. This First Amendment shall become effective on the date (such date, the “First Amendment Effective Date”), when each of the following conditions is satisfied (or waived in accordance with Section 12.02):

5.1 The Administrative Agent shall have received from the Required Lenders and the Borrower, counterparts (in such number as may be requested by the Administrative Agent) of this First Amendment signed on behalf of such Person.

5.2 The Administrative Agent and the Lenders shall have received all fees and other amounts due and payable on or prior to the date hereof, including, to the extent invoiced, reimbursement or payment of all documented out-of-pocket expenses required to be reimbursed or paid by the Borrower under the Credit Agreement.

5.3 No Default shall have occurred and be continuing as of the date hereof, after giving effect to the terms of this First Amendment.

5.4 The Administrative Agent shall have received such other documents as the Administrative Agent or its special counsel may reasonably require.

The Administrative Agent is hereby authorized and directed to declare this First Amendment to be effective when it has received documents confirming or certifying, to the satisfaction of the Administrative Agent, compliance with the conditions set forth in this Section or the waiver of such conditions as permitted in Section 12.02. Such declaration shall be final, conclusive and binding upon all parties to the Credit Agreement for all purposes.

Section 6. Miscellaneous.

6.1 Confirmation. The provisions of the Credit Agreement, as amended by this First Amendment, shall remain in full force and effect following the effectiveness of this First Amendment.

6.2 Ratification and Affirmation; Representations and Warranties. The Borrower and each Guarantor hereby (a) acknowledges the terms of this First Amendment, (b) ratifies and affirms its obligations under, and acknowledges its continued liability under, each Loan Document to which it is a party and agrees that each Loan Document to which it is a party remains in full force and effect as expressly amended hereby and (c) represents and warrants to the Lenders that as of the date hereof, after giving effect to the terms of this First Amendment:

(i) all of the representations and warranties contained in each Loan Document to which it is a party are true and correct in all material respects (except those which have a materiality qualifier, which shall be true and correct as so qualified), except to the extent any such representations and warranties are expressly limited to an earlier date, in which case, such representations and warranties shall continue to be true and correct as of such specified earlier date, and

(ii) no event or events have occurred which individually or in the aggregate could reasonably be expected to have a Material Adverse Effect.

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6.3 Counterparts. This First Amendment may be executed by one or more of the parties hereto in any number of separate counterparts, and all of such counterparts taken together shall be deemed to constitute one and the same instrument. Delivery of this First Amendment by facsimile transmission or electronic transmission in portable document format (.pdf) shall be effective as delivery of a manually executed counterpart hereof.

6.4 NO ORAL AGREEMENT. THIS FIRST AMENDMENT, THE CREDIT AGREEMENT AND THE OTHER LOAN DOCUMENTS EXECUTED IN CONNECTION HEREWITH AND THEREWITH REPRESENT THE FINAL AGREEMENT BETWEEN THE PARTIES AND MAY NOT BE CONTRADICTED BY EVIDENCE OF PRIOR, CONTEMPORANEOUS, OR UNWRITTEN ORAL AGREEMENTS OF THE PARTIES. THERE ARE NO SUBSEQUENT ORAL AGREEMENTS BETWEEN THE PARTIES.

6.5 GOVERNING LAW. THIS FIRST AMENDMENT SHALL BE GOVERNED BY, AND CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF TEXAS.

6.6 Payment of Expenses. In accordance with Section 12.03 of the Credit Agreement, the Borrower agrees to pay or reimburse the Administrative Agent for all of its reasonable out-of-pocket costs and reasonable expenses incurred in connection with this First Amendment, any other documents prepared in connection herewith and the transactions contemplated hereby, including, without limitation, the reasonable fees and disbursements of counsel to the Administrative Agent.

6.7 Severability. Any provision of this First Amendment which is prohibited or unenforceable in any jurisdiction shall, as to such jurisdiction, be ineffective to the extent of such prohibition or unenforceability without invalidating the remaining provisions hereof, and any such prohibition or unenforceability in any jurisdiction shall not invalidate or render unenforceable such provision in any other jurisdiction.

6.8 Successors and Assigns. This First Amendment shall be binding upon and inure to the benefit of the parties hereto and their respective successors and assigns.

6.9 Loan Document. This First Amendment is a Loan Document.

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IN WITNESS WHEREOF, the parties hereto have caused this First Amendment to be duly executed as of the date first written above.

[Signature Page First Amendment]

[Signature Page First Amendment]

[Signature Page First Amendment]