Karl Hawley headed United into the lead before the half-time break, after the away side had dominated the opening half.
However, Bury hit back in the second and levelled midway through it via a Jonson Clarke-Harris free-kick, before former Iron loanee Nicky Ajose scored just two minutes later.
They couldn't find a way back into the game and, with two games left to play, now find themselves five points behind Oldham Athletic, who have a game in hand.
The Iron entered the game making no changes from the side that drew 1-1 with Walsall.
Eirik Holmen Johansen started in goal, with Eddie Nolan, Paul Reid, Niall Canavan and Tom Newey forming the defence.
The midfield consisted of Mark Duffy, Michael Collins, Jimmy Ryan and Anthony Forde, while Karl Hawley and Matt Godden led the attack.
The substitutes were Sam Slocombe, Christian Ribeiro, David Mirfin, Akpo Sodje, Mike Grella, Robbie Gibbons and James Alabi.
The Iron were quick out of the blocks and got off to a quick start, with Hawley turning and firing a shot into Cameron Belford's hands.
They continued to press and then, in the seventh minute, Canavan saw his header saved from Reid's cross from the left side.
However, he needed to receive treatment after injuring his nose getting the effort in and he was replaced by Mirfin four minutes later.
On 18 minutes, Duffy then cut in from the right and fizzed in a shot which was tipped wide for a corner.
The Iron continued to apply the most pressure as the game reached the midway stage of the first half and it was at this point when they came close again, as Hawley saw his close range drive blocked away after good link-up play on the left.
Then, just two minutes later, Godden sprung the offside trap after being played through and clipped his volley past the onrushing Belford, but wide of goal.
He then got played through again on 26 minutes, this time with Hawley alongside him, and he played his partner in whose deflected effort was tipped wide by Belford.
From the subsequent corner, Mirfin saw his header blocked and Collins fired wide of goal.
The hosts forced a save from Johansen on the half hour mark as Mark Carrington's low drive from the edge of the area was stopped.
Tom Soares was next to register an effort on goal for the hosts in the 37th minute, firing an effort well wide from distance.
As the first half drew to a close, United forced a further corner as Collins' drive was deflected behind but nothing of note came from it.
The final Bury chance of the opening period came the Shakers' way with a minute left as a free-kick deflected off Zac Thompson and out for a goal-kick.
But there was still one more opportunity to be had as Scunthorpe took the lead on 45 minutes. Duffy's floating free-kick from the right was glanced home by Hawley for his eighth goal of the season - and Scunthorpe's first strike away from home since January.
They came close two minutes into the second half but Mirfin headed wide from a Duffy free-kick.
On 53 minutes, after good work from the strike pairing of Godden and Hawley, Duffy received the ball on the right side of the area but rushed his shot and drilled wide.
The away side continued their pressure and Newey's free-kick caused danger in the 18-yard box as it was deflected wide.
The hosts came close on 60 minutes when Ajose's tame effort from six yards, after a left-wing cross, was held by Johansen.
Then, Reid stopped the danger as he diverted a dangerous David Worrall cross wide for a corner, from which nothing arose.
Nevertheless, the home side continued their pressure and they levelled on 66 minutes through a free-kick from Jonson Clarke-Harris, whose free-kick from the right side of the 18-yard box flew beyond the dive of Johansen.
And three minutes later it was 2-1 as Ajose came back to haunt his former club. The striker was played through by Carrington and prodded beyond the dive of the advancing Johansen.
This prompted a double Scunthorpe change as Grella replaced Forde and Sodje came on for Hawley.
United tried to force their way back into the game but Bury were resolute and this meant the away side left gaps open at the back.
Ajose came close again on 82 minutes as he was played through and drilled an effort wide at the near post after attacking from the left side.
And he had another chance with three minutes left as he cut in from the left before fizzing an attempt wide of goal.
There were four minutes of stoppage time but no further chances as Scunthorpe fell to defeat.
Bury: Belford, Eastham, Worrall, Carrington, Ajose, Hughes, Regan, Clarke-Harris, Thompson, Soares, Mezague.
Substitutes not used: Healy, Pratt.
Scunthorpe United: Johansen, Nolan, Reid, Canavan (Mirfin, 12), Newey, Duffy, Collins, Ryan, Forde (Grella, 68), Hawley (Sodje, 70), Godden.
Substitutes not used: Slocombe, Ribeiro, Gibbons, Alabi.
Attendance: 1,567 (248 away).