Wolves boasted two changes from the side that beat Watford 2-0 in the Premier League at the weekend as Ruben Neves and Morgan Gibbs-White replaced Leander Dendoncker and Adama Traore.
Besiktas were hit by the loss of former Tottenham man Georges-Kevin N’Koudou because of an injury in the warm-up and he was replaced by Caner Erkin.
The hosts started brightly but it took them until the 17th minute to pose a real threat in the final third when Guven Yalcin picked up possession from Jeremain Lens down the right and hit a teasing cross into the centre which Conor Coady hacked clear.
Wolves went close on 28 minutes when Pedro Neto’s cross from the left took a nick off Domagoj Vida on the way through and keeper Loris Karius, on loan from Liverpool, was forced to make a smart stop at his near post.
On 34 minutes, Lens got the better of Jonny out on the right before delivering a cross to Erkin who made a mess of his effort at goal.
Coady was fortunate not to concede an own goal on 42 minutes when he deflected a corner into the Wolves area against the post, before Rui Patricio got down to save at the feet of Mehmet Nayir just before the break.
Wolves had the first chance of note after the break with Raul Jimenez getting up to meet a Joao Moutinho free-kick but he could only direct his header over the crossbar.
On 63 minutes Moutinho delivered a dangerous corner into the box which the unmarked Boly got on the end of, but again the effort was just too high to trouble Karius.
Wolves continued to look the more likely to open the scoring and Romain Saiss was next to try his luck with a thunderous 30-yard strike which Karius was forced to push away to safety.
Besiktas finally issued a response as Vida won a header from a free-kick into the Wolves’ box but it dropped inches wide of Patricio’s goal, before he sent another header off target on 72 minutes.
Wolves hit back as substitute Patrick Crutrone curled a shot just wide of Karius’ far corner on 83 minutes, before Saiss bundled the ball into the Besiktas net in the final minute only for the offside flag to deny him.
However, the visitors were not to be denied as Boly scored with virtually the last kick of the game when he impressively brought down a Neves ball into the area before turning and firing beyond the dive of Karius.
The win leaves Wolves third in the group, but they are just a point behind leading pair Slovan Bratislava and Braga.