The Imps had new boy Craig Westcarr to thank for the three points.
The youngster, signed on loan from Nottingham Forrest, marked his debut by netting the 24th minute winner.
Westcarr found himself unmarked inside the box and after controlling a pass from Gary Taylor-Fletcher picked his spot from 15 yards.
Lincoln struggled to master the blustery conditions but had chances to increase their lead.
Westcarr had a low shot saved at his near post by Bury keeper Andy Marriott.
Then a mistake by Danny Swailes let in Taylor-Fletcher but the striker's shot was blocked by Colin Woodthorpe.
Lincoln were threatening to over-run Bury and created an excellent chance in the 35th minute. Taylor-Fletcher set up Richard Butcher but from 15 yards the midfielder sent his shot over the bar.
Four minutes later Bury almost equalised when David Nugent hit in a low shot which brought a great save from Marriott.
Kevin Sandwith then fired a shot into the Bury box but Jamie McCombe was inches away from connecting.
Sandwith created more danger in the 53rd minute when his corner picked out Francis Green at the far post but Marriott was on hand to save.
Bury went close in the 63rd minute when Terry Dunfield touched a free-kick on to Simon Whaley but the midfielder's shot crashed narrowly wide.
Play quickly swung to the other end and three minutes later Bury were saved by Marriott.
The veteran keeper made a superb block to keep out a shot from Sandwith but when the ball came back to Ciaran Toner the Irish international blasted over the bar.
Nugent, expected to move to a bigger club in the next few weeks, twice went close late on.
But Lincoln still looked dangerous and Green had the ball in the net in the 74th minute only for his effort to be ruled out for offside.