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                                                                     EXHIBIT 5.1
 
                  [COTTON, BLEDSOE, TIGHE & DAWSON LETTERHEAD]
 
                                 April 17, 1998
 
Costilla Energy, Inc.
400 West Illinois, Suite 1000
Midland, Texas 79701
 
          Re: Registration Statement on Form S-4
 
Gentlemen:
 
     We have acted as counsel for Costilla Energy, Inc., a Delaware corporation
(the "Company") in connection with the registration under the Securities Act of
1933, as amended (the "Act"), of $80,000,000 in aggregate principal amount of
the Company's 10 1/4% Senior Notes due 2006 (the "Notes"), to be exchanged for
certain outstanding 10 1/4% Senior Notes due 2006. A Registration Statement on
Form S-4 covering the issuance and sale of Notes was filed under the Act with
the Securities and Exchange Commission (the "Commission") on April 17, 1998 (the
"Registration Statement").
 
     In reaching the conclusions expressed in this opinion, we have examined
signed copies of the Registration Statement and all exhibits thereto. We have
also examined and relied upon originals, or copies certified to our
satisfaction, of (i) the Certificate of Incorporation and Bylaws of the Company,
(ii) minutes and records of the corporate proceedings of the Company with
respect to the issuance of the Notes and related matters, and (iii) such other
agreements and instruments relating to the Company as we have deemed necessary
or appropriate for the purposes of the opinions hereinafter expressed. In
rendering such opinions, we have relied, to the extent we deemed reasonable, on
certificates and certain other information provided to us by officers of the
Company and public officials as to matters of fact of which the maker of such
certificates or the person providing such information had knowledge, without
investigation into or verification of such information. Furthermore, we have
assumed that the signatures on all documents examined by us are genuine, that
all documents and corporate record books submitted to us as originals are
authentic, accurate and complete, and that all documents submitted to use as
copies are true, correct and complete copies of the originals thereof.
 
     Based solely upon the foregoing, subject to the assumptions, limitations
and qualifications set forth herein, and specifically limited in all respects to
the laws of the State of Texas, of the United States of America and the General
Corporation Law of the State of Delaware, we are of the opinion that the Notes
registered pursuant to the Registration Statement have been duly and validly
authorized by the Company and, when paid for, issued, exchanged or sold and
delivered in accordance with the terms of the Registration Statement, will be
binding obligations of the Company, subject to applicable bankruptcy,
insolvency, reorganization, fraudulent transfer, moratorium or similar laws
affecting creditors' rights generally and to general principles of equity and
the availability of equitable remedies. Please note in this regard that we are
not licensed to practice law in the State of Delaware, but have reviewed
Delaware law in connection with the opinions expressed herein.
 
     We hereby consent to the use of this opinion as an exhibit to the
Registration Statement and to the reference to this Firm under the caption
"Legal Matters" in the Prospectus forming a part of the Registration Statement.
In giving this consent we do not thereby admit that we come within the category
of persons whose consent is required under the Act or the rules and regulations
of the Commission promulgated thereunder.
 
     This opinion is rendered only to the Company and solely for the benefit of
the Company and the Commission in connection with the registration and the
issuance of the Notes pursuant to the Registration Statement. This opinion may
not be otherwise used, circulated, quoted, relied upon, or referred to by you or
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the Commission for any other purpose or by any other person, firm or corporation
for any purpose, without our prior written consent.
 
                                                     Yours very truly,
 
                                              COTTON, BLEDSOE, TIGHE & DAWSON
 
                                            By:   /s/ RICHARD T. MCMILLAN
 
                                              ----------------------------------
                                                     Richard T. McMillan