Lincoln were under pressure from the off and goalkeeper Alan Marriott produced a succession of saves before finally being beaten by Aaron McLean claiming his 30th goal of the campaign on 18 minutes.
Earlier, Marriott denied George Boyd at point-blank range after advancing to take the sting out of a McLean effort, before defender Nat Brown swept the ball off the line.
Marriott was powerless to stop McLean crashing a shot into the roof of the net, despite denying both Boyd and Chris Whelpdale immediately before.
Then Marriott had to go full length to palm another McLean effort past his right-hand post.
Although Lincoln failed to trouble Posh goalkeeper Joe Lewis before the break, their defensive cause was helped by some sloppy home shooting with McLean, Whelpdale and Boyd all failing to make the most of good openings.
It took Posh just four second-half minutes for McLean to grab his second with Lincoln down to ten men as Paul Green received treatment.
As the floodgates opened Scott Rendell (56), on loan from Cambridge United, scored his first Posh goal from the tightest of angles and then fired a second through the legs of Marriott on 68 minutes.
Substitute Jamie Forrester produced some late attacking flair for Lincoln, but Posh held firm and at the other end Brown produced his second goal-line clearance of the game to prevent Whelpdale joining the scoring spree.