They netted twice in eight minutes and had another goal disallowed as Lincoln struggled to stay in the game.
City could have been in front after just four minutes when Derek Asamoah set up Paul Mayo but the midfielder shot well wide from a good position.
Peterborough were quick to hit back with Adam Newton holding off a challenge before putting Danny Crow away, Crow had only the keeper to beat but somehow shot wide.
Then a poor back pass from Lincoln defender Lee Beevers set up another chance for United. His error let in James Quinn and created another opening for Crow only for the striker's shot to be charged down by Lincoln skipper Paul Morgan.
Lincoln tried to get back into the game and midfielder Dean Keates went close with a 25-yard shot which Peterborough keeper Mark Tyler pushed over the top.
Peterborough got the ball in the net in the 24th minute when Quinn scored direct from a free kick but referee Gary Lewis ruled the effort out because he had not blown his whistle to restart the game.
Peterborough were unlucky when crow saw a 56 minute shot blocked by the legs of city keeper Alan Marriott.
But five minutes later Lincoln cracked after Carden was fouled by Scott Kerr just outside the box. Kerr was yellow carded and from the free-kick Quinn headed home from close range.
Within 60 seconds Crow had the ball in the Lincoln net again but the goal was disallowed for offside.
Peterborough kept up the pressure and were rewarded when the hardworking Gain fired in a cross of which was bundled home by Newton.
United almost added a third goal eight minutes from the end when substitute Trevor Benjamin beat Marriott with a header but Jamie McCombe cleared off the line.
Lincoln suddenly woke up and pulled a goal back when Keates scored with a speculative overhead kick. Peterborough finished the game with only 10 men when Carden, booked for the first half foul, picked up his second yellow card when he went in late on Keates.