Bury were almost caught napping in the early stages when an error by Mick Nelson allowed Steve Torpey in but Lee Unsworth swept the ball from his feet.
Unsworth then got in a block on a Scott Brough attempt while Ian Kilford was well of the mark.
However, Kilford went closer in the 18th minute when his right-foot shot crashed over the top off the crossbar.
The Shakers had made little impression and their first effort came after half an hour bur Preece's effort was well off target.
Scunthorpe had a golden opportunity to take a 37th minute lead when they were awarded a penalty.
Chris Billy was adjudged to have pulled down Torpey but Martin Carruthers' spot kick was a poor one, going out of play past the right-hand post and never testing goalkeeper Glyn Garner.
Kilford again went close with a free-kick from deep on the left and it was flicked over the top by the keeper.
Scunthorpe remained in control after the break. Unsworth cleared off the line from Carruthers and he repeated the dose when Jamie McCombe followed up and Lee Ridley drifted a free kick over the top.
Bury eventually began to show a little bit more interest in going forward and Billy's free-kick failed to trouble Tommy Evans.
However, they took the lead in the 72nd minute when Preece knocked a free-kick low into the box and Danny Swailes beat the home defence to turn the ball in from close range.
Shakers boss Andy Preece said afterwards: "At times we were never at the races and our first-half display was totally unacceptable.
"We had 15 minutes in the game where we played and when you get the pressure you have to score which we did."Scunthorpe's manager Brian Laws said: "I couldn't have asked for more from my players.
"We were running away with it, but they got the breaks by putting bodies all over the place and the goal came as a result of a ball that was very difficult to deal with."