The home side’s leading scorer, who had gone seven league games without a goal, struck after 18 minutes, firing into the bottom corner after poor Shakers defending.
On-loan Blackpool forward Daniel Nardiello equalised on the stroke of half-time, heading home from a corner for his fourth goal in six games for the Gigg Lane club.
The game caught fire after the break as Nardiello hit the crossbar from close range, while Andy Morrell lifted the ball over with just Tony Roberts to beat.
John Still’s side were back in front after 78 minutes when Peter Gain sent the ball over from the left, John Scott’s shot was saved by keeper Wayne Brown, only for Benson to turn in the rebound.
The home made sure of the points in injury time as on-loan Chelsea full-back Nana Ofori-Twumasi combined with Benson, before drilling low past Wayne Brown.