Okan Buruk's side occupy the final relegation place and are three points adrift with one game remaining after defeat to Besiktas, confirmed through Gokhan Tore's strike.
Elazigspor will be without Ibrahim Kas when they face Rizespor next week, the defender saw red less than 15 minutes after coming off the bench against Slaven Bilic's men, who remain in third, one point behind second-place Galatasaray.
Gaziantepspor are still not safe despite ending a run of four consecutive defeats with a 1-1 draw against Eskisehirspor.
They went ahead after 61 minutes through Cenk Tosun and were on course to secure their survival but conceded a last minute Necate Ates goal, which leaves them three points ahead of Elazigspor, but with a worse head to head record.
Kayseri Erciyesspor got the point they needed to guarantee survival in the 1-1 draw with Bursaspor.
Edinho's 11th of the season in first-half injury time set them on their way and although Ozan Ipek equalised in the 89th minute, Kayseri Erciyesspor are safe thanks to a superior head to head record over Elazigspor.
At the other end of the table, Galatasaray thumped Trabsonspor 4-1 to remain second and dent their opponents' hopes of finishing in the UEFA Europa League places.
All goals came in the second half, which included a Wesley Sneijder brace, and a goal each from Selcuk Inan and Umut Bulut.
Adrian Mierzejewski scored a penalty to give Trabzonspor hope at 2-1 but Roberto Mancini's men ran away with it to record a fourth straight win.
Sivasspor took advantage of that slip with 3-1 win over Akhisar Belediyespor.
The visitors went ahead despite being down to 10 men after Wato Kuate's red card. Kerim Zengin got the goal but Sivasspor hit back in style with a brace from John Utaka and an injury time strike by the league's top goalscorer, Aatif Chahechouhe - his 17th of the season.
Champions Fenerbahce hammered Karabukspor 4-0, with Moussa Sow, Raul Meireles, Emre and Pierre Webo all on the scoresheet.
Elsehwere, Kasimpasa drew 1-1 with Rizespor, while already relegated Antalyaspor defeated Genclerbirligi 2-1.
Bottom club Kayserispor lost 3-0 at Konyaspor, with their misery compounded after Sefa Yilmaz's red card.
