City, unbeaten in their opening eight games, have now lost three out of four and looked completely out of form.
Bury, in contrast, were sharp and first to every ball, controlling the game from the start.
Winger Marc Pugh caused the Lincoln defence problems all afternoon and went close in the 17th minute when he turned a defender before firing a shot narrowly wide.
Five minutes later Andy Bishop tried his luck from the edge of the box, but his shot was saved by Lincoln keeper Alan Marriott.
Bury continued to dominate and went close in the 39th minute when Bishop rose above the Lincoln defence to head towards goal. His effort beat Marriott only to be cleared off the line by Scott Kerr.
The Shakers finally broke the deadlock in the 43rd minute after Lincoln defender Paul Mayo was penalised for bringing down Pugh on the edge of the box.
Thomas Kennedy's free-kick found Pugh and his shot was charged down. But the ball fell kindly for Richie Baker, who swept home his shot from the edge of the box for his first senior goal.
Lincoln continued to struggle after the break and always looked in danger of conceding another goal.
A 49th-minute corner from Pugh was flicked into the side-netting by Dwayne Mattis, with the Lincoln defence mere spectators.
Then, a great ball from David Buchanan sent Bishop racing clear, but Marriott was quickly out of his area to hack the ball away.
Bury grabbed a richly deserved second in the 54th minute. Kennedy swung over a cross from the left which was headed home by Glynn Hurst, despite Marriott's efforts to keep it out.
Lincoln finally started to look like their old selves in the last 20 minutes. Lee Beevers set up Jamie Forrester, but the striker's powerful shot was beaten away by Kasper Schmeichel.
The young goalkeeper then did well to keep out the follow-up effort from Mark Stallard.
A long throw from Beevers was headed on by Stallard but, from six yards out, Forrester sent his header over the bar.
Lincoln's final chance came in stoppage-time, when Stallard smashed in a shot from ten yards, but Schmeichel tipped it over the bar.