David Flitcroft's men were one of three sides able to leapfrog Burton on Saturday, who lost 3-1 to Cambridge United the day before, but only they collected a win to move them a point clear.
Kelvin Etuhu struck his first goal for the club since arriving from Barnsley to give Bury the lead on 55 minutes, the midfielder collected the ball outside the penalty area and fired beyond Owain Fon Williams from distance.
The victory was assured with three minutes to play as Daniel Nardiello met a Chris Hussey corner to head home from close range.
Wycombe Wanderers missed the chance to go top as they were held to a 1-1 draw by Northampton Town at Adams Park.
Ryan Cresswell put the visitors ahead a minute after the half hour and that looked to have secured all three points until the eighth minute of stoppage time when Aaron Holloway rescued a point for Wycombe.
Southend United were the other side capable of taking first place but they fell to a fourth defeat of the season at the hands of Morecambe, Jack Redshaw netting the only goal at Roots Hall.
Keith Curle's revolution at Carlisle United continues to gather pace as they recorded back-to-back victories and moved off the foot of the table.
Goals from Steven Rigg, Stephen Elliott and Mark Beck earned them a 3-0 win over Hartlepool United, who drop to the bottom.
Oxford climbed away from the danger zone with a 1-0 win over Newport County, while Accrington Stanley collected a third-straight win under John Coleman thanks to a Luke Joyce penalty after Sascha Studer had fouled Marcus Carver.
Plymouth Argyle's 1-0 win over Shrewsbury Town moves them closer to the top seven, where Luton Town are two points clear of them after a 2-1 win at Stevenage.
Cheltenham Town were denied a first league win since the end of August as Adam Barrett earned AFC Wimbledon a 1-1 draw, while York City played out a third goalless draw of the season against Portsmouth.