Second-half goals from Aydin Karabulut and Burhan Eser.condemned Fenerbahce to a second sucessive defeat and Ersun Yanal's men have been beaten three times in their last five games.
The visitors were reduced to 10 men after 22 minutes when defender Egemen Korkmaz was dismissed, and fourth-placed Sivasspor capitalised in the second period with strikes from midfielders Karabulut and Eser.
Fenerbahce's fierce rivals Galatasaray closed the gap at the summit on Saturday, easing to a comfortable 3-0 home win against Eskisehirspor.
First-half efforts from striker Burak Yilmaz and defender Aurelien Chedjou put Roberto Mancini's side in command, before Umut Bulut put the gloss on a fine performance with an injury-time strike.
Third-placed Beskitas remain in the hunt for a place in the UEFA Champions League after goals from midfielder Olcay Sahan and attacker Omer Sismanoglu ensured a 2-1 success at Gaziantepspor on Friday.
Karabukspor stay two points behind fourth-placed Sivasspor in the battle for a UEFA Europa League spot by virtue of Monday's 2-1 away win against Genclerbirligi.
Mehmet Akyuz stole the show as Akhisar Belediyespor won a 4-2 thriller at Trabzonspor.
The 28-year-old forward scored a second-half hat-trick after Ugur Demirok's 16th minute opener had been cancelled out by Olcan Adin, who netted a consolation for the hosts in the second minute of time added on.
Serdar Ozkan and Deniz Yilmaz each scored penalties as Elazigspor moved out of the bottom three with a 3-0 triumph over 10-man bottom club Kayserispor, while Rizespor dropped into the relegation zone after a 1-1 draw with fellow-strugglers Kayseri Erciyesspor.
Elsewhere, a Theofanis Gekas double inspired Konyaspor to a 3-1 victory at Kasimpasa, and Bursapsor drew 1-1 with Antalyaspor.
