The Shakers came from behind to secure this overdue victory.
There was an error-strewn opening spell at Gigg Lane, before Stanley finally opened up on 13 minutes.
Sean Webb rose well but headed Peter Cavanagh's corner-kick over the crossbar, before Graham Branch stormed down the left before flashing a low shot wide of the far post.
Bury hit back when Glynn Hurst's shot was saved well by Kenny Arthur, but the visitors were on top and they were denied by the woodwork on 23 minutes.
Ian Craney - making his second debut for Accrington after returning from Swansea during the week - found space before thumping a superb 25-yard shot against the Bury crossbar.
The ball bounced down, hit the back of Bury keeper Jim Provett and went out for a corner.
Just beyond the half-hour mark, Bury's Brian Barry-Murphy floated in a free-kick and Paul Scott got in a decent header but Arthur gathered the ball at the second attempt.
Scott then had a great chance to open the scoring on 38 minutes. Barry-Murphy obliged again with another good cross, but the unmarked Shakers midfielder somehow blasted a shot over the bar from close range.
Amazingly Accrington took the lead just 60 seconds after the restart.
A hopeful ball forward saw Bury defender Ben Futcher try to clear the danger, but his attempt simply cannoned off the head of the onrushing Paul Mullin and the ball looped into the empty net for the big targetman's fifth goal of the season.
Minutes later, Branch was unmarked but he shot well over.
Bury got themselves back on terms on 71 minutes when substitute Andy Mangan intercepted a poor Paul Carden back pass then rounded the keeper before slotting home neatly.