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Derrick Williams managed to get in behind the City backline early on, but the decision to square the ball rather than taking the shot ultimately proved costly.
Wolves were enjoying plenty of the ball in the opening stages, coming close through Dave Edwards who powered a header wide, while some smart link-up play by James Henry and Dominic Iorfa also offered promise.
The Robins, who were on the end of a thrashing last time out here, soon grew into things and were looking particularly lively through Luke Freeman after he was afforded plenty of space to operate in.
That came shortly after Edwards had a goal correctly ruled out for offside, but it was not all the visiting side's way as Kieran Agard - starting in place of Aaron Wilbraham this evening - forced Martinez into action up the other end.
City came close to bagging themselves a second of the game through lively top-scorer Kodjia, who this time shot low across goal for Martinez to get down and save.
It was proving to be a frustrating night for Jackett and his men, largely due to a failure to create any real attacking moves when chasing a goal.
Matt Doherty was introduced for Wanderers with 12 minutes left to play, allowing Henry to push further upfield where he could get in a couple more shots.
Yet a late Doherty penalty shout aside, Wolves could not muster any real threat as City held out to claim the win which lifts them four points clear of the relegation zone.