The Stags, who remain in the bottom two, had looked to be on course for their first Field Mill win since Boxing Day when captain Jake Buxton slammed in from close range ten minutes into the second half and moments after Micky Boulding struck the post.
Keeper Carl Muggleton then preserved the lead with a string of fine saves as Bury, who have not lost to Mansfield since 2003, fought back well.
But he had no chance when Rooney's 84th minute overhead kick continued the Shakers' revival under new manager Alan Knill.
Bury had piled on the early pressure, no doubt aware of the Stags' recent atrocious home form.
But it was the swirling gale which dominated the opening minutes as both sides struggled to take set-pieces because of the strength of the wind.
From the second of successive Mansfield corners whipped in on the wind, Boulding's flying header was acrobatically beaten away by the flying Darren Randolph.
At the other end, Andy Bishop's terrific drive from a Nicky Adams flick-on just grazed the bar from a long Randolph clearance.
Then on a swift counter-attack, former County striker Glynn Hurst poked his finish narrowly past the post with keeper Muggleton beaten.
However, the Stags finished the half the stronger and from a deep Hamshaw cross Jefferson Louis nodded agonisingly wide at the far post after climbing above two defenders.
Mansfield continued to carry the greater threat at the start of the second half with Atkinson hooking a shot over from ten yards and Boulding almost converting a quickly taken Hamshaw free-kick.
Then Boulding's clever shot on the turn, after spinning past Efe Sodje, struck the foot of the post and Keith Briggs' goalbound follow-up was blocked.
But Mansfield's pressure finally told in the 55th minute when Buxton smashed the breakthrough from close range at the second attempt in a remarkable goalmouth melee.
First Louis' close-range header was somehow turned around the post by the scrambling keeper.
Randolph repeated his heroics to beat out Briggs' header from the following corner and then block Buxton's follow-up, but when the ball fell kindly for Buxton a second time, he made no mistake from five yards to fire into the roof of the net.
Elliott Bennett's 20-yard piledriver was stopped at the second attempt by Muggleton as Bury pressed hard for a leveller and then the midfielder saw another long-range effort well held.
Muggleton dived spectacularly to his right to beat away a Sodje thunderbolt and did even better to tip over another crashing Bennett drive as the keeper stood between the Shakers and an equaliser.
But he had no chance six minutes from time as Bury deservedly gained reward for their fightback.
Yet another long range drive, this time from Paul Scott, was deflected high into the area and substitute Rooney dramatically sent his overhead kick into the bottom corner.