Skipper Steve Schumacher fired the visitors into a deserved lead after 12 minutes with a well struck free-kick that took a deflection off the defensive wall to beat keeper Steve Mildenhall.
It was reward for a good start from the Shakers as Scunthorpe, with new loan signing Mark McChrystal making his debut at the centre of the defence on loan from Tranmere, struggled to get their game together.
In a poor first half showing, the best Scunthorpe could muster was a blistering long range shot from leading marksman Leon Clarke that brought the best out of keeper Trevor Carson.
Clarke did get the home side back on level terms in the 52nd minute when he burst into the box from the right and steered a measured left foot shot into the bottom far corner past keeper Trevor Carson.
Bury were back in front less than a minute later when a low cross from the left by Troy Hewitt sliced open a poor home defence for Troy Hewitt to force the ball home from close range.
The introduction of Nathan Ellington from the substitutes' bench breathed new life into Scunthorpe.
With his first touch he set up a good chance for Clarke, which he dragged wide.
Then keeper Trevor Carson produced a great reaction save from midfield man Josh Walker to deny Scunthorpe a point as they slipped to their first defeat in four games since new manager Brian Laws took charge.