Slaven Bilic's side fell behind when Cedric Bakambu put the fourth-placed visitors in front with a composed finish after racing clear 12 minutes in.
The prolific Ba struck 11 minutes later with a clinical strike and the Istanbul side were in front for the first time when Gokhan Tore found the back of the net with a stunning right-foot strike three minutes from time.
There was still plenty more drama to come, though, and Ozan Tufan looked to have salvaged a point when he volleyed home with 90 minutes played, only for there to be one final twist.
As Kerim Frei raced into the penalty area Sener Ozbayrakli tugged the substitute back and was shown a red card before Ba held his nerve to score his 22nd goal of the season from the penalty spot and secure all three points nine minutes into time added on.
Second-placed Fenerbahce had no such trouble as they dished out a 5-0 hammering to Gaziantepspor on Saturday.
Moussa Sow scored twice in the space of eight second-half minutes, while Emmanuel Emenike, Dirk Kuyt and Emre Belozoglu (penalty) were also on target as Fenerbahce took their frustration out on Gaziantepspor after losing top spot by drawing with Trabzonspor seven days earlier.
Third-placed Galatasaray have now won eight games in a 10-match unbeaten league run after they beat 10-man Balikesirspor 3-1 on Monday courtesy of first-half goals from Aurelien Chedjou, Wesley Sneijder and Burak Yilmaz.
Bottom-of-the-table Balikesirspor must have been braced for a hammering when Aykut Ceviker was shown a second yellow card just after the hour-mark, but they showed character and Ermin Zec scored a consolation 10 minutes from time.
Trabzonspor moved above Istanbul Basaksehir into fifth place by consigning them to a 3-2 defeat to move level on points with Bursaspor.
Eskisehirspor moved out of the relegation zone by winning 2-1 at Genclerbirligi on Monday, Karabukspor are also out of the bottom three on goal difference following their goalless draw at Kasimpasa on Saturday
Rizespor dropped to second-bottom following their 4-0 hammering at home to Mersin Idmanyurdu, while Kayseri Erciyesspor find themselves in the drop zone courtesy of a 1-0 loss at Akhisar Belediye.
Sivasspor beat Konyaspor 1-0 in Sunday's mid-table encounter.
