Stanley suffered their second consecutive league defeat on their travels in a match that was overshadowed by a serious looking injury to full back Nicky Hunt.
Hunt was stretchered off just before the hour mark after receiving lengthy medical attention with what looked like a knee problem.
The victory means Bury’s fine home record over their M66 rivals continues.
James Beattie’s first derby match as Stanley manager started in typically frantic fashion, with both sides going close early on.
The hosts were almost ahead in the first minute when Jordan Sinnott’s right-wing cross fortuitously hit the bar, much to the relief of the travelling fans behind the goal.
In the sixth minute, the visitors should have taken the lead. Laurence Wilson’s cross was deflected and fell to Kal Naismith who missed at the far post. Will Hatfield met the rebound but saw his shot hit the post.
Shakers boss Kevin Blackwell lamented his side’s bad fortune in their opening league games prior to the match, and their first half performance supported his claims.
On 28 minutes, Bury opened the scoring courtesy of a quick free-kick that caught the Reds defence napping. Sinnott’s pass was met by Anton Forrester, who was able to tap home from close range.
The saying it never rains it pours rang true at Gigg Lane for Accrington, as just five minutes later, experienced forward Danny Webber was dismissed for a late challenge on Bury’s Shaun Beeley.
With their tails up, the Shakers took advantage of the extra man as well as some poor Stanley defending. Craig Jones’ right-wing cross was intercepted by Hatfield who, with his back to goal could only gift the ball to the ever-present Sinnott on the left who fired home with a precise finish.
The visitors were unfortunate not to win a penalty when Shakers skipper Gareth Roberts appeared to handle a Hunt cross five minutes shy of the interval.
The half-time whistle seemed to come at the right time for Stanley though, who re-grouped and were the superior side in the second period.
Kal Naismith’s effort from the edge of the penalty area was well held by Bury stopper Rob Lainton after the restart and moments later, Rob Atkinson’s looping header from a corner was within inches of reducing the deficit.
Just shy of the hour came the derby’s main talking point. An innocuous coming together between Forrester and Hunt ended with the defender on the floor in serious pain, needing treatment from medical staff from all sides of the ground. After a lengthy treatment stoppage, he was taken away from the pitch to applause from all four sides of the ground.
Beattie brought on Michael Richardson who unnerved the Bury backline, and Accrington continued to press but could not find an end product.
Despite their dominance, ten men Stanley were always susceptible to the counter attack and that was the case for Bury’s third goal on 87 minutes.
Against the run of play, substitute Marlon Jackson latched onto Craig Jones’ right-wing cross and he chested the ball down, turned and produced a low shot past Dunbavin to add some gloss to the scoreline for the hosts. It was harsh on Stanley after their positive second half showing.
Stanley: Dunbavin, Hunt (Winnard 66) , Aldred, Atkinson, Liddle (McCartan 46’), Joyce, Murphy, Naismith, Hatfield ( Richardson 71’), Wilson, Webber
Subs: Winnard, McCartan, Richardson, Miller, Clark, Mingoia, Gray