A first-half free-kick strike from Steven Schumacher gave the Shakers the lead before top scorer Leon Clarke levelled proceedings early in the second half.
However, the hosts' joy would quickly turn sour when with Bury's next attack they restored their lead with Tom Hopper tapping in from close range.
Scunthorpe made two changes for the visit of Bury with Josh Walker and debutant Mark McChrystal coming in for Jimmy Ryan and the suspended Paul Reid.
Steve Mildenhall remained in goal with a defence of Christian Ribeiro, Niall Canavan, McChrystal and Tom Newey.
The midfield consisted of Mark Duffy, Walker, Damien Mozika and Andy Barcham while Leon Clarke partnered Karl Hawley up front.
The substitutes' bench meanwhile was made up of Sam Slocombe, Callum Kennedy, Ryan, Mike Grella, Robbie Gibbons, Callum Howe and Nathan Ellington.
The Iron were nearly behind in under 60 seconds when Canavan's poor back pass was intercepted by Hewitt who only had the goalkeeper to beat. Luckily for the Iron though Mildenhall was sharp off his line and blocked his poked effort.
It was the visitors once again in the tenth minute when Zac Thompson met a Tom Hopper cutback only to fire his effort a couple of yards over the bar.
But Bury wouldn't be stopped a few minutes later when they deservedly took the lead through Steven Schumacher. After the Iron had given away a free kick just outside the box Schumacher stepped up to blast and hit the back of the net via a huge deflection to give the Shakers the lead.
Canavan came to the rescue in the 18th minute when he managed to deflect Hopper's shot on the penalty stop to stop what would have been a certain goal.
Clarke nearly equalised for the Iron with their first effort on goal in the 22nd minute. Only a fine reaction save from Carson kept Clarke's powerful volley from the edge of the box equaling proceedings after Hawley had flicked the ball superbly into the path of the on-loan striker.
Hawley marauding run down the byline nearly levelled the game with ten minutes of the first half remaining.
Picking the ball up just inside the box, the 30-year-old took his player to the byline before poking across goal, only to see his effort deflect off a Bury defender and trickle inches wide of the goalkeeper's far hand post.
Matt Doherty almost doubled the Shakers' lead in the 39th minute but his shot on the turn from inside the box was dragged a few yards wide of the post.
Hopper should have doubled Bury's lead a few minutes after half time but his glancing header towards the goalkeeper's right hand post narrowly missed the back of the net.
Clarke would make the visitors pay for their misses minutes later when he equalised for the Iron out of nothing.
Again it was the combination between Hawley and Clarke that paid dividends with Hawley flicking on for Clarke down the left with the only the goalkeeper to beat.
There, Clarke showed composure to pass the ball across the keeper into the bottom right hand corner.
The Iron wouldn't remain on level terms for long though as Tom Hopper put the visitors back ahead with their attack from the kick-off.
This time, Hewitt broke down the left hand side using his pace before sliding into the box where an unmarked Hopper was there to tap home from close range.
Clarke nearly got the Iron back into it with 25 minutes to go but his near post header could only hit the side netting.
The Iron made their first substitutions of the game shortly after when Hawley and Barcham were replaced with Kennedy and Ellington.
It was Clarke once again in the 68th minute but after Ellington had done well to nod the ball down to Clarke, the striker could only drag his left footed effort wide of the post without troubling the goalkeeper.
A well rehearsed set play involving three players nearly got the Iron level as they started to put the visitors under heavy pressure. After winning a free kick on the edge of the box, Kennedy dummied to shoot before a cheeky Mark Duffy pass was laid into the path of Walker who's powerful effort fortunately for Bury was well palmed away by the goalkeeper.
They made their final change with 12 minutes to go when Damien Mozika was replaced by Jimmy Ryan.
Mildenhall had to be at his best with eight minutes to go though when an instinctive strike from Soares from the edge of the box was brilliantly clawed away by the keeper.
Bury made their first change of the match seconds after when Tom Hopper was replaced by Lenell John-Lewis.
And with minutes left they made their final change bringing on veteran Efe Sodje in place of Hewitt.
There were no more real chances as Scunthorpe, who are next in action when they visit Doncaster at the weekend, suffered defeat.
Scunthorpe United: Mildenhall, Ribeiro, McChrystal, Canavan, Newey, Duffy, Walker, Mozika (Ryan 78), Barcham (Kennedy 67), Hawley (Ellington 67), Clarke.
Substitutes not used: Slocombe, Grella, Gibbons, Howe.
Bury: Carson, Doherty, Hughes, Ebanks-Landell, Skarz, Worrall, Thompson, Schumacher, Hewitt (Sodje 90), Soares, Hopper (John-Lewis 83).
Substitutes not used: Belford, Sweeney, Jones, Carrington, Jones.
Iron Bar man of the match: Leon Clarke.
Sponsors' man of the match: Mark Duffy.
Attendance: 3,027 (242 away).