Super Lig Wrap: Emre spot on for Fenerbahce
After a goalless first half, the 33-year-old struck after 57 minutes and made sure of the win for Ersun Yanal's side with 19 minutes remaining when he fired home from the spot again.
The result maintained the hosts' push for the title while piling the pressure on nearest rivals Galatasaray, who failed to play their part 24 hours later.
Galatasaray are now six points behind the leaders after they could only manage a 1-1 draw at Rizespor.
Roberto Mancini's side took the lead after 61 minutes through Aurelien Chedjou - scorer against Chelsea in the UEFA Champions League in midweek - but their hopes suffered a huge blow four minutes from time when substitute Leonard Kweuke scored from the spot to give the hosts a much-needed point in their survival bid.
Meanwhile, Besiktas slipped further off the pace as they could only manage a goalless draw at home to Antalyaspor - with Slaven Bilic's side remaining third, now eight points behind the leaders.
Sivasspor's winless run in all competitions was extended to four games as they went down 3-1 at home to Elazıgspor.
Deniz Yilmaz struck an early penalty for the visitors and although Burhan Eser equalised after 33 minutes, Elazigspor put the game beyond the hosts with two goals in three second-half minutes.
Mehmet Akyuz's brace was enough to give Akhisar Belediyespor a 2-1 win over Bursaspor, while Trabzonspor could only manage a goalless draw at Konyaspor.
They join Karabukspor on 34 points, who lost 1-0 at home to Gaziantepspor after conceding an early goal to Abdou Razak Traore.
The weekend's relegation battle was won by Kayseri Erciyesspor, who thumped bottom club Kayserispor 4-0.
The two sides could not be separated early on but the visitors went in front through Edinho just before half time and the Portuguese attacker struck again after 55 minutes.
He was replaced by Senijad Ibricic 13 minutes from the end and the Bosnian notched a brace of his own within 10 minutes.