Exhibit 5.1

201 ST. CHARLES AVENUE NEW ORLEANS, LOUISIANA 70170-5100 504.582.8000 FAX 504.582.8583 www.joneswalker.com

November 27, 2013

CenturyLink, Inc.

100 CenturyLink Drive

Monroe, Louisiana 71203

Ladies and Gentlemen:

We have acted as special counsel for CenturyLink, Inc., a Louisiana corporation (the “Company”), in connection with the issuance and sale of $750,000,000 aggregate principal amount of 6.75% Senior Notes, Series W, due 2023 (the “Notes”), pursuant to the Underwriting Agreement, dated as of November 14, 2013 (the “Underwriting Agreement”), entered into by and among the Company and Wells Fargo Securities, LLC and the other underwriters named in Schedule I therein, as underwriters (collectively, the “Underwriters”). The Notes will be issued pursuant to the Indenture, dated as of March 31, 1994 (the “Original Indenture”), by and between the Company and Regions Bank (successor to First American Bank & Trust of Louisiana), as trustee (the “Trustee”), as heretofore supplemented by board resolutions and as further supplemented by supplemental indentures, including the Ninth Supplemental Indenture dated as of November 27, 2013 by and between the Company and the Trustee (the “Supplemental Indenture” and, together with the Original Indenture, as so supplemented through the date hereof, the “Indenture”).

In connection with the opinion expressed herein, we have examined the Notes, the Underwriting Agreement and the Indenture (the “Transaction Agreements”) and such documents, records and matters of law as we have deemed relevant or necessary for purposes of such opinion. In conducting our examination, we have assumed without verification the legal capacity of all natural persons, the genuineness of all signatures, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as certified, conformed or photostatic copies, the authenticity of the originals of such copies, the due authorization, execution and delivery of all documents by all parties other than the Company, and the validity, binding effect and enforceability thereof on all such parties. As to various questions of fact material to this opinion, we have relied without independent verification upon (i) the accuracy of certificates and other comparable documents of officers and representatives of the Company, (ii) representations and warranties made by the Company in the

	JONES WALKER LLP
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November 27, 2013

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Underwriting Agreement, (iii) statements made to us in discussions with the Company’s management and (iv) certificates of public officials.

Based on the foregoing, and subject to the further limitations, qualifications and assumptions set forth herein, we are of the opinion that the Notes, when they are duly authenticated by the Trustee in accordance with the Indenture and issued and delivered to the Underwriters against payment therefor in accordance with the terms of the Underwriting Agreement, will constitute valid and binding obligations of the Company.

For purposes of the opinion expressed herein, we have assumed that (i) the definitive terms of the Notes will be established in accordance with the provisions of the Indenture, (ii) the Trustee has duly authorized, executed and delivered the Original Indenture and the Supplemental Indenture, and is qualified under the Trust Indenture Act of 1939, and (iii) the Indenture is the valid, binding and enforceable obligation of the Trustee.

The opinion expressed herein is subject to the qualification that enforceability may be limited by (i) applicable bankruptcy, insolvency, fraudulent transfer, reorganization, moratorium or similar laws of general applicability relating to or affecting the enforcement of creditors’ rights, (ii) general principles of equity (regardless of whether enforceability is considered in a proceeding in equity or at law), including without limitation concepts of materiality, reasonableness, good faith and fair dealing, (iii) public policy considerations that may limit the rights of parties to obtain certain remedies, (iv) laws or public policy considerations that may limit the enforceability of provisions relating to indemnification, exculpation or contribution, (v) governmental authority to limit, delay or prohibit the making of payments outside of the United States or in a foreign currency or currency unit, (vi) the effects of applicable laws requiring the mitigation of damages and (vii) the possible unenforceability of contractual provisions providing for choice of governing law or venue, permitting only written contract modifications or waivers, granting or limiting rights of third parties, providing for the waiver of unmatured rights, permitting parties to enforce rights without providing an opportunity to cure, or permitting terms of a contract to be severed.

We do not express any opinion herein concerning any law other than the Louisiana Business Corporation Law (including the statutory provisions and reported judicial decisions interpreting the foregoing). We express no opinion as to the application of (i) the securities or blue sky laws of the various states to the sale of the Notes, (ii) securities or other laws of any foreign nation or jurisdiction and any rules and regulations promulgated thereunder, (iii) the rules of the Financial Industry Regulatory Authority or (iv) any law, rule or regulation that is applicable to any party to the Transaction Agreements or the transactions contemplated thereunder solely because such law, rule or regulation is part of a regulatory regime applicable to such party or any of its affiliates as a result of the specific assets or business operations of such party or its affiliates.

In addition, in rendering the foregoing opinion, we have assumed that neither the execution and delivery by the Company of the Transaction Agreements nor the performance by the Company of its obligations thereunder (i) constitutes or will constitute a violation of, or a

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default under, any lease, indenture, instrument or other agreement to which the Company or its property is subject, (ii) contravenes or will contravene any order or decree of any governmental authority to which the Company or its property is subject, (iii) violates or will violate any law, rule or regulation to which the Company or its property is subject or (iv) requires the consent, approval, licensing or authorization of, or any filing, recording or registration with, any governmental authority under any law, rule or regulation of any jurisdiction.

This letter has been furnished in accordance with applicable rules promulgated by the Securities and Exchange Commission (the “Commission”), and is expressly limited to the specific legal issues addressed herein. We render no opinion, whether by implication or otherwise, as to any factual matter or any other legal matter relating to the Company, the Transaction Agreements or any of the other transactions discussed hereunder. This letter is not and should not be deemed to be a warranty that a court considering any legal issue addressed herein would not rule in a manner contrary to the opinion set forth above. This letter speaks only as of the date hereof. We assume no obligation to revise or supplement this letter should presently applicable laws be changed by legislative action, judicial decision or otherwise.

We consent to the filing of this letter as Exhibit 5.1 to the Current Report on Form 8-K dated the date hereof filed by the Company and incorporated by reference into the Company’s Registration Statement on Form S-3 (Registration No. 333-179888) (the “Registration Statement”), and to the reference to Jones Walker L.L.P., New Orleans, Louisiana, under the caption “Legal Matters” in the prospectus supplement dated November 14, 2013 describing the Notes and constituting a part of the Registration Statement. In giving this consent, we do not admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act of 1933, as amended, or the general rules and regulations of the Commission.

Very truly yours,

/s/ Jones Walker L.L.P.

JONES WALKER L.L.P.