Luke Williams was the hero for United, as he won the game for the visitors with a free-kick four minutes from time.
There was one alteration from Saturday's clash with Bradford, as Williams replaced Gary McSheffrey.
As for the rest of the starting eleven, things were left unchanged. Luke Daniels remained the man between the sticks, and in front of him was a back four of Scott Wiseman, David Mirfin, Niall Canavan and Scott Laird.
Jack King and Neal Bishop were once again United's central midfield pairing, and in front of them were Williams, Tommy Rowe and Paddy Madden, who were the main support to striker Darius Henderson.
It was a fairly slow start to proceedings, but the Iron got their noses in front, inside of 11 minutes. After taking the ball superbly out the air, Williams drove into the Shakers' penalty area and was cynically pulled to the ground, leaving referee Tony Harrington with no choice but to point to the penalty spot.
Madden stepped up and emphatically dispatched the spot-kick into the bottom right corner, to give United an early lead.
The hosts instantly went looking for an equaliser, and they went close on two occasions in the space of a minute. Firstly, Leicester loanee Joe Dodoo forced Daniels into a fine save, with a deflected effort from the edge of the box.
Then former Iron man Leon Clarke looked to have found the back of the net, with a neat effort. However, the Bury striker could only tuck his shot around the outside of the goal.
It was an impressive response from David Flitcroft's side, but they weren't having any luck in breaking down United. This was no more evident than when Danny Rose rounded Daniels, but despite having the goal at his mercy, he could only find the outside of the post.
Having soaked up the hosts' pressure, the Iron almost doubled their lead just after the half an hour mark. Madden was sent through on goal after a loose pass from Danny Pugh. The Irishman tricked his way through, and tested Daniel Bachmann with a low drive.
There would be one final scare for United before the break, when Clarke latched onto a throughball. However, the Shakers frontman was denied by a good reaction stop from Daniels.
Mark Robins' side did well to preserve their lead, and even though luck may have been with them on a few occasions, they went in ahead at the interval.
Five minutes into the second period though, the hosts were level. Joe Riley showed some neat footwork to skip past Laird, and he then delivered a cross on a plate for Clarke, who placed the ball into the top right hand corner.
The equaliser sparked United into life once more, and they almost re-took the lead immediately, through King. The midfielder was foiled twice by Bachmann in a short space of time. Firstly the Austrian blocked a close range shot from King, and he was then back on his feet to claw the United vice-captain's far post header away.
The United number 18 was frustrated again shortly after. This time he arrived late into the penalty area, and got on to the end of a Henderson pull-back, but some last ditch defending from the Shakers denied him.
Much like the home side in the first half, the Iron were the team in the ascendancy. Rowe was next to test Bachmann, but the Bury 'keeper showed good reactions to push the midfielder's left footed strike away.
Clarke, who had already found the net once, should have found it again 20 minutes from time. The striker was put clean through on goal, and had time to set himself. Despite this, he made poor contact with the ball and dragged his effort wide.
A piece of genius so nearly got the visitors back in front, 10 minutes from time. Williams pinched the ball inside of his own half and then went on a marauding run. But after beating four Shakers defenders, he couldn't beat Bachmann, who foiled the midfielder as he burst into the box.
The diminutive playmaker wasn't to be denied though, as with four minutes to play, he curled a free-kick expertly into the bottom right hand corner of Bachmann's goal. It was no more than the former Middlesbrough man deserved, after turning in an impressive display throughout.
The visitors were resolute and held on for a superb victory.
Bury: Bachmann, Riley, Hussey, Clarke, Etuhu, Clarke, Jones (Eagles, 85), Pugh, Cameron, Rose (Pope, 69), Dodoo.
Substitutes not used: Ruddy, Sedgwick, Burgess, Brown.
Scunthorpe United: Daniels, Wiseman, Mirfin (Goode, 34), Canavan, Laird (Clarke, 56), Bishop, King, Williams, Rowe, Madden, Henderson.
Substitutes not used: Anyon, McAllister, van Veen, Adelakun, McSheffrey.
Attendance: 2,483 (189 away).
Tweets by @SUFCOfficial