Umut Bulut put the hosts ahead four minutes in, before Belarus equalised through Vitali Rodionov just six minutes later.
Both teams hit the frame of the goal as they went in search of a winner, but it was not until the 89th that Yilmaz gave Turkey the victory, leaving Belarus with just one win from their last five outings.
Aykut Demir and Umut Bulut came in for Semih Kaya and Mehmet Topal as Fatih Terim made two changes to the Turkey side that beat Northern Ireland 1-0 on Friday, while Aleksandr Hleb and Aleksandr Martynovich were among five alterations to the Belarus XI that drew 0-0 with Albania.
Turkey made the dream start, breaking the deadlock in the fourth minute when Caner Erkin pulled the ball back for Bulut to power beyond Aleksandr Gutor from 10 yards.
But the visitors were soon level as former Barcelona midfielder Hleb provided the assist for Rodionov to scoop an effort into the top left-hand corner.
And Rodionov almost put Belarus ahead in the 29th minute, but was denied from close range by an excellent reaction save from Tolga Zengin, who touched the ball onto his left-hand post.
The remainder of the half failed to live up to the end-to-end opening, as both sides struggled to make any inroads into the opposition defence.
That was until the 44th minute when Arda Turan attempted an audacious lob from 25 yards, only to be denied by the crossbar.
Belarus were on the attack from the off in the second half, with Demir making a crucial interception from a Rodionov cross.
At the other end, Turan then sent a powerful half-volley goalwards from the edge of the penalty area in the 52nd minute, but Gutor managed to push it over his crossbar.
Turkey were having the better of the possession after the break, but Belarus went close to edging ahead in the 65th minute as Sergey Balanovich fired into the side-netting, before Timofey Kalachev forced a save from Zengin and Stanislav Dragun headed agonisingly wide of the target.
Gokhan Gonul crossed in from the right in the 74th minute, only to find Mevlut Erding who failed to apply a good enough finish as Gutor made the block.
Balanovich was then presented with a glorious opportunity to net a winner 11 minutes from time, but a wild swing of the leg saw him fail to make a meaningful connection as Turkey made the clearance.
And Yilmaz made Belarus pay for their wasted opportunities one minute from time, when Gutor failed to hold onto his initial effort and the striker made no mistake at the second time of asking.
Syarhey Kislyak sent a free-kick just wide of the target before the final whistle, but it proved to be the visitors' last chance of the match.
