Besiktas moved into a 1-0 lead in Sunday's encounter at the Recep Tayyip Erdogan Stadium when Olcay Sahan scored on the half-hour mark.
Slaven Bilic's men were pegged back just after the hour as Sinan Kaloglu levelled for Mersin.
Ba's initial shot was saved by Nikolay Mihaylov, but the ball rebounded back off the striker, who had fallen to the floor, and spooned into the net for his 10th league goal of the campaign.
Galatasaray slipped three points off the pace on Sunday after being held 2-2 at home by Bursaspor.
The visitors overcame Umut Bulut's early opener to move ahead thanks to goals from Volkan Sen and Fernandao.
However, third-placed Gala rescued a draw through Emre Colak's 82nd-minute penalty.
Fenerbahce remained top of the table after winning 2-1 at struggling Karabukspor on Saturday to stretch their unbeaten league run to 12 matches.
Selcuk Sahin put the visitors ahead in the seventh minute, before Emmanuel Emenike ended a near three-month wait for a league goal in the second half to down his former team. The Nigeria international later apologised to the Karabukspor supporters for celebrating his goal.
Akhisar Belediyespor were held 2-2 at home by Balikesirspor on Friday and Trabzonspor defeated Kayseri Erciyesspor 2-1.
