Exhibit 5.1

October 28, 2014

Ingersoll-Rand plc

170/175 Lakeview Dr.

Airside Business Park

Swords, Co. Dublin

Ireland

Ladies and Gentlemen:

We have acted as United States counsel to Ingersoll-Rand plc, an Irish public limited company (“IR-plc”), Ingersoll-Rand Company Limited, a Bermuda company (“IR-Limited”), Ingersoll-Rand International Holding Limited, a Bermuda company (“IR-International”), Ingersoll-Rand Global Holding Company Limited, a Delaware corporation (“IR-Global”), Ingersoll-Rand Company, a New Jersey corporation (“IR-Company” and, together with IR-plc, IR-Limited, IR-International and IR-Global, the “Guarantors”) and Ingersoll-Rand Luxembourg Finance S.A., a Luxembourg public company limited by shares (société anonyme) (the “Issuer” and, together with the Guarantors, the “IR Entities”), in connection with the Registration Statement on Form S-3 (File No. 333-199562) (the “Registration Statement”) filed by the IR Entities with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), and the issuance by the Issuer of $300,000,000 aggregate principal amount of 2.625% Senior Notes due 2020 (“2020 Notes”), $500,000,000 aggregate principal amount of 3.550% Senior Notes due 2024 (“2024 Notes”) and $300,000,000 aggregate principal amount of 4.650% Senior Notes due 2044 (“2044 Notes” and together with the 2020 Notes and the 2024 Notes, the “Notes”), in each case, unconditionally guaranteed by the Guarantors pursuant to the Underwriting Agreement, dated October 23, 2014 (the “Underwriting Agreement”), among the Issuer, the Guarantors and the several underwriters named there.

We have examined the Registration Statement; the IR Entities’ prospectus dated October 23, 2014 (the “Base Prospectus”), as supplemented by the prospectus supplement dated October 23, 2014 (together with the Base Prospectus, the “Prospectus”), filed by the IR Entities pursuant to Rule 424(b) of the rules and regulations of the Commission under the Securities Act; the Indenture, dated as of October 28, 2014 (the “Base Indenture”), as amended and supplemented by the first supplemental indenture, dated as of October 28, 2014 (the “2020 Notes Supplemental Indenture”), relating to the 2020 Notes, as further amended and supplemented by the second supplemental indenture, dated as of October 28, 2014 (the “2024 Notes Supplemental Indenture”), relating to the 2024 Notes and as further amended and supplemented by the third supplemental indenture, dated as of October 28, 2014 (the “2044 Notes Supplemental Indenture” and, together with the Base Indenture, the 2020 Notes Supplemental Indenture and the 2024 Notes Supplemental Indenture, the “Indenture”), relating to the 2044 Notes, among the Issuer, the Guarantors and The Bank of New York Mellon, as trustee (the “Trustee”); duplicates of the global notes representing the Notes; the guarantees annexed to each Note (the “Guarantees”); and the Underwriting Agreement. In addition, we have examined, and have relied as to matters of fact upon, originals, or duplicates or certified or conformed copies, of such records, agreements, documents and other instruments and such certificates or comparable documents of public officials and of officers and representatives of the IR Entities and have made such other investigations, as we have deemed relevant and necessary in connection with the opinions hereinafter set forth.

In rendering the opinions set forth below, we have assumed the genuineness of all signatures, the legal capacity of natural persons, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as duplicates or certified or conformed copies, and the authenticity of the originals of such latter documents.

In rendering the opinions set forth below, we have assumed further that (1) the Issuer, IR-plc, IR-Limited, IR-International and IR-Company are validly existing and in good standing under the law of Luxembourg, Ireland, Bermuda and New Jersey, as applicable, and have duly authorized, executed and delivered the Underwriting Agreement, the Indenture, the Notes and the Guarantees, as applicable, in accordance with their respective certificate of incorporation (or equivalent instrument) and bye-laws and the law of Luxembourg, Ireland, Bermuda and New Jersey, as applicable, (2) the execution, delivery and performance by the Issuer, IR-plc, IR-Limited, IR-International and IR-Company of the Underwriting Agreement, the Indenture, the Notes and the Guarantees, as applicable, do not violate the law of Luxembourg, Ireland, Bermuda, New Jersey or any other jurisdiction, except that no such assumption is made with respect to the federal law of the United States or the law of the State of New York, and (3) the execution, delivery and performance by the Issuer, IR-plc, IR Limited, IR International and IR Company of the Underwriting Agreement, the Indenture, the Notes and the Guarantees, as applicable, do not constitute a breach or violation of, or require any consent to be obtained under, any agreement or instrument which is binding upon the Issuer, IR-plc, IR-Limited, IR-International and IR-Company or their respective certificate of incorporation (or equivalent instrument) and bye-laws.

Based upon the foregoing, and subject to the qualifications, assumptions and limitations stated herein, we are of the opinion that:

1. The Notes have been duly executed and issued by the Issuer in accordance with the law of the State of New York and, assuming due authentication of the Notes by the Trustee, and upon payment and delivery in accordance with the Underwriting Agreement, the Notes will constitute valid and legally binding obligations of the Issuer, enforceable against the Issuer in accordance with their terms and entitled to the benefits of the Indenture.

2. The Guarantees have been duly executed and issued by the Guarantors in accordance with the law of the State of New York and, assuming the due authentication of the Notes by the Trustee, and upon payment for and delivery of the Notes in accordance with the Underwriting Agreement, each Guarantee will constitute a valid and legally binding obligation of the applicable Guarantor, enforceable against such Guarantor in accordance with its terms and entitled to the benefits of the Indenture.

Our opinions set forth above are subject to (i) the effects of bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium and other similar laws relating to or affecting creditors’ rights generally, (ii) general equitable principles (whether considered in a proceeding in equity or at law), (iii) an implied covenant of good faith and fair dealing and (iv) the effects of the possible judicial application of foreign laws or foreign governmental or judicial action affecting creditors’ rights. In addition, we express no opinion as to the validity, legally binding effect or enforceability of (A) the waiver of rights and defenses contained in Sections 117(b) and 1301(b) of the Base Indenture or (B) Section 110 of the Base Indenture and Section 304 of each of the 2020 Notes Supplemental Indenture, the 2024 Notes Supplemental Indenture and the 2044 Notes Supplemental Indenture relating to the severability of provisions of the Indenture.

In connection with the provisions of the Indenture and the Underwriting Agreement under which the Issuer and the Guarantors submit to the jurisdiction of any U.S. federal court in the Borough of Manhattan, The City of New York, we note the limitations on original jurisdiction of the U.S. federal courts under 28 U.S.C. §§ 1331 and 1332. In connection with the provisions of the Indenture and the Underwriting Agreement which relate to forum selection (including, without limitation, any waiver of any objection to venue or any objection that a court is an inconvenient forum), we note that under NYCPLR §510 a New York State court may have

discretion to transfer the place of trial and under 28 U.S.C. §1404(a) a U.S. District Court has discretion to transfer an action from one U.S. federal court to another. We also note that the recognition and enforcement in New York State courts or U.S. federal courts sitting in the State of New York of a foreign judgment obtained against the Issuer and the Guarantors is subject to the Uniform Foreign Money—Judgments Recognition Act (53 C.P.L.R. §5301 et. seq.).

We do not express any opinion herein concerning any law other than the law of the State of New York, the federal law of the United States and the Delaware General Corporation Law.

We hereby consent to the filing of this opinion letter as Exhibit 5.1 to the Current Report on Form 8-K of IR-plc filed with the Commission in connection with the offer and sale of the Notes by the Issuer and to the use of our name under the caption “Legal Matters” in the Prospectus included in the Registration Statement.