Exhibit 5.1

January 30, 2014

Textron Inc.

40 Westminster Street

Providence, Rhode Island 02903

Ladies and Gentlemen:

We have acted as counsel for Textron Inc., a Delaware corporation (the “Company”), in connection with the issuance and sale by the Company of $250,000,000 principal amount of its 3.65% Notes due March 1, 2021 and $350,000,000 principal amount of its 4.30% Notes due March 1, 2024 (collectively, the “Notes”) pursuant to the Underwriting Agreement dated January 23, 2014 between the several underwriters named therein (the “Underwriters”) and the Company (the “Agreement”). The Notes are being issued under the Indenture dated as of September 10, 1999 between The Bank of New York Mellon Trust Company, N.A. (as successor to The Bank of New York), as trustee (the “Trustee”), and the Company (including the form and terms of the Notes established in the Officers’ Certificate of the Company dated the date hereof pursuant to Section 3.1 thereof, the “Indenture”).

We have reviewed (a) the Agreement, (b) the Indenture, (c) the Registration Statement on Form S-3 (File No. 333-175886) (the “Registration Statement”) filed by the Company to register the Notes with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933 (the “Act”) and (d) the Prospectus dated July 29, 2011, as supplemented by the Prospectus Supplement dated January 23, 2014, relating to the offer and sale of the Notes (as so supplemented, the “Prospectus”) filed by the Company with the Commission pursuant to Rule 424(b)(2) under the Act. We have also reviewed such other agreements, documents, records, certificates and other materials, and have satisfied ourselves as to such other matters, as we have considered relevant or necessary as a basis for this opinion.

In such review, we have assumed the accuracy and completeness of all agreements, documents, records, certificates and other materials submitted to us, the conformity with the originals of all such materials submitted to us as copies (whether or not certified and including facsimiles), the authenticity of the originals of such materials and all materials submitted to us as originals, the genuineness of all signatures and the legal capacity of all natural persons. In delivering this opinion, we have relied, without independent verification, as to factual matters, on certificates and other

written or oral statements of governmental and other public officials and of officers and representatives of the Company, the Underwriters and the Trustee.

On the basis of the assumptions and subject to the qualifications and limitations set forth herein, we are of the opinion that the Notes constitute the valid and legally binding obligations of the Company enforceable against the Company in accordance with their terms, except as may be subject to and limited by the effect of (a) applicable bankruptcy, insolvency, reorganization, fraudulent conveyance and other similar laws affecting creditors’ rights generally, (b) general equitable principles (whether considered in a proceeding in equity or at law) and (c) requirements of reasonableness, good faith, materiality and fair dealing and the discretion of the court before which any matter may be brought.

This opinion is limited to the law of the State of New York and the General Corporation Law of the State of Delaware, in each case as in effect on the date hereof.

We hereby consent to the filing of this opinion as Exhibit 5.1 to the Company’s Current Report on Form 8-K filed by the Company with the Commission on the date hereof and the incorporation thereof in the Registration Statement and to the use of our name under the captions “Legal Opinions” and “Legal Matters” in the Prospectus Supplement. In giving this consent, we do not thereby admit that we are within the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Commission promulgated thereunder.

Very truly yours,

/s/ Pillsbury Winthrop Shaw Pittman