Tom Thorpe tucked away the winning spot-kick after an entertaining game as Wayne Rooney's brother John netted twice for the home side and, although James Wilson and two-goal Will Keane were on the scoresheet, Anthony Dudley forced a the shoot-out with an 80th-minute leveller.
The Reds could have few complaints about trailing at half time after struggling to make any in-roads towards Brian Jensen's goal. Reece James, recently recalled from his loan with Carlisle, shot well wide after Will Keane headed on a Larnell Cole pass but most of the noteworthy moments came at the other end.
A poor kick-out by Jonny Sutherland was beyond Charni Ekangamene and Greg McDermott fed Rooney for an unerring finish that punished the visitors with 23 minutes on the clock. Referee Simon Mather decided Guillermo Varela did not handle in the box afterwards, despite Bury's appeals, and Marcos Navas, brother of Manchester City's Jesus, flashed a drive off target.
Five minutes before the interval, Steve Jennings connected at the back post with a volley that thumped against the bar as the Shakers were good value for their lead. United needed to respond following Warren Joyce's team-talk and Andreas Pereira was unable to provide a finish to match a purposeful run.
An equaliser was forthcoming following a first move of genuine quality from the holders. Thorpe burst out of defence to allow Will Keane to intelligently nudge the ball wide to Varela. The Uruguayan slipped a perfect through ball into the path of Wilson, who poked past the advancing Jensen in confident fashion.