A wicked wind blowing hard down the pitch swept so much of the skill out of the game for the first hour and no one found it harder to cope than Bristol's Brazilian keeper Adriano Basso.
With defenders failing to clear Wolves first corner right on half-time, he hesitated as Michael Kightly whipped in a ball from the left and Neil Collins made him pay for his indecision with his fourth goal of the season.
Results had already gone Wolves' way before the evening kick-off and they looked set for a ninth away win and a double over last season's play-off finalists.
Until their goal, a shapeless half had produced just two shots - one too straight from City's Slovakian signing Peter Styvar and a 30-yard cross-shot from Wolves' left-back Matt Hill, whose career began at Ashton Gate.
With wind and now rain on their backs, Wolves looked to have the points sewn up early in the second half when Matt Jarvis latched on to a through ball from Kightly to fire a clean drive into the bottom right-hand corner.
With Basso redeeming himself with saves from Sylvan Ebanks-Blake and Jarvis, Wolves were completely on top, but reckoned without Adebola.
He had replaced Styvar at the break to give City more muscle, but he provided that just four minutes after Jarvis' strike as, fed by Nicky Maynard, he powered through a channel to the left of the visitors' goal.
Wayne Hennessey in goal had no chance with his shot and suddenly it was game on.
Believing in themselves for the first time, City pounded the Wolves defence with Adebola saving the day for them late on with an unselfish square ball for Maynard to ram home.