Ryan Lowe's first-half brace set Bury on course for a 3-0 win over nine-man Accrington.
The Lancashire rivals went into the game in the League Two play-off places but Stanley were outclassed as they failed to repeat the form that saw them beat Gillingham 7-4 last week.
Lowe opened the scoring in the 13th minute with his 100th career league goal. Phil Edwards failed to deal with a long clearance and Lowe poked the ball past Ian Dunbavin from 12 yards.
He claimed his ninth of the season just before the break by sweeping Phil Picken's cut-back inside the far post.
On-loan Manchester United forward Nicky Ajose sealed the victory when he cut inside Johnny Bateson and tucked away his first senior goal in the 57th minute.
Andy Procter was sent off 15 minutes from time after clashing with Damien Mozika and Bateson joined him in the bath for a dangerous tackle on Kyle Bennett.