A second-half goal from striker Mark Stallard proved decisive in a tight game, which was dominated for long spells by the visitors.
But Posh, under new manager Darren Ferguson, had only themselves to blame for not getting at least a share of the points, as they wasted a string of chances.
Peterborough then faded badly once Lincoln were in front and City comfortably held on for the three points. The defeat was Peterborough's eighth consecutive League loss and means their chances of making the top three at the end of the season has almost completely disappeared.
Peterborough had an excellent chance to break the deadlock after three minutes when George Boyd set up Josh Low. The winger had only the keeper to beat but lifted his shot over the bar from close range.
Low then got a great cross in from the left which found the head of Aaron McLean, but the striker's effort was deflected wide.
Then an excellent flick from Boyd put Peter Gain into the box, but the midfielder overran the ball.
Lincoln showed little in the way of threat until the second half, but should have gone in front in the 50th minute. The Peterborough defence was caught out by a cross from Ryan Amoo and the ball fell kindly for Stallard, but the striker delayed his shot and Adam Newton nipped in to clear.
Boyd then got crowded out by the Lincoln defence before McLean sent in a weak effort from 30 yards.
Lincoln got the only goal of the game in the 70th minute when they won a corner after a powerful shot from Paul Mayo deflected off two defenders. Lee Frecklington sent the ball over to the far post, where the unmarked Stallard grabbed his 12th goal of the season with a firm header.
Lincoln's Jamie Forrester was denied by a diving save from Mark Tyler before Lee Beevers had a header blocked on the line.
Peterborough lost their influential midfielder and captain Micah Hyde with a leg injury, but despite late pressure could not force an equaliser.