Scott Wiseman fired in the opening goal of the game on 42 minutes, but Tom Soares responded with a close range goal thirteen minutes after the break.
The game was settled on 64 minutes when Morris picked out the top corner of the goal for the away side, a goal worthy of winning any game.
Early pressure from the Shakers could easily have led to a goal in the first seven minutes of the match. Zeli Ismail found the target after cutting in from the right flank, but his shot was well saved by Luke Daniels at his near post.
Tom Pope was next to threaten the Scunthorpe goal, his header in front of goal could only rattle the crossbar after an excellent ball in from Neil Danns down the left wing.
The return of former Shakers favourite, Stephen Dawson, almost ended with the Irishman finding the first goal of the match as he had the audacity to shoot from the right side of the penalty area towards Ben Williams’ front post, however, his shot was equalled by Williams and the post combined.
The visitors found the opener as another ex-Shaker, Tom Hopper, was involved in the mix as he squared the ball back into the Bury penalty area and Irons’ defender Scott Wiseman was on hand to smash the ball into the back of the net.
Although, the lead did not last long for Scunthorpe. Ismail’s drilled ball across the penalty area was not dealt with, Soares pounced on the ball and drove the ball past Daniels for the equalising goal.
Scunthorpe were in the lead once again soon after, Josh Morris followed up on his hat-trick in midweek with a curling left footed shot from 25 yards out that flew into the top left corner of Williams’ goal.
Morris tried his luck again just eight minutes later. His shot replicated his goal as the ball curled goalwards for the left side of the target but this time it could not beat the upright.
On 76 minutes, Jacob Mellis came very close to bringing the game back to level terms, his low and powerful shot from 25 yards out found the target, but Daniels was quickly down to his right to deny an equaliser.
The lead could have been extended further as Kevin Van Veen picked out an unmarked Sam Mantom inside the penalty area, yet his shot was well saved and held by the safe hands of Williams.
The Shakers will look to bounce back on Tuesday evening as they travel to Bradford City for their second game of the Checkatrade Trophy.
Attendance:5,355 (864 away fans)
Bury starting line-up:Williams, Leigh, Maher (Etuhu 82), Bryan, Kay, Ismail, Danns (Walker 55), Mellis, Soares, Hope (Dudley 67), Pope
Unused subs:Tutte, Burgess, Rachubka, Bedeau
Scunthorpe United starting line-up:Daniels, Wiseman, Mirfin, Wallace, Dawson, Morris (Goode 90+1), Bishop, Hopper, Toffolo, Smallwood (Mantom 82), Holmes (Van Veen 77)
Unused subs:Madden, Anyon, Adelakun, Townsend