Sherwin Seedforf, Benny Ashley-Seal and Will Randall netted in the second-half to send Wolves through with a game to spare.
It meant Joseph Adams’ opener for Bury, which arrived straight after the interval, counted for nothing and Wolves travel to Bournemouth on Monday with the pressure off.
Seedforf had looked the most likely throughout and struck the post early on with a fine strike, while Conor Levingston forced the experienced Joe Murphy into a simple save soon after.
Levingston’s free-kick again called Murphy into action, while Adams’ effort from a clever free-kick sailed harmlessly over the bar for Bury.
Straight after the break the same man slid home the opener from close range for Bury, but Wolves produced the perfect response just ten minutes later.
Terrific strength by Seedorf hold off his man and race in on goal, and he kept his composure to slot home the equaliser past Murphy.
Wolves tails were up and Randall cut on to his right foot and tested Murphy, before the pressure told on 69 minutes.
Eight minutes after coming on, Ashley-Seal was hauled down in the box, giving the referee little decision but to point to the spot. The striker dusted himself down and fired underneath Murphy from 12 yards.
The scoring was complete just three minutes later, as Randall finally got himself on the scoresheet by firing home with his right foot to confirm the victory.
