They had the better of the opening half but both teams found it difficult to create chances. Lincoln should have gone in front in the 43rd minute when Francis Green set up Simon Yeo. The striker failed to hit the target from 10 yards with only the keeper to beat.
But Lincoln changed things round at the break and never looked back after the introduction of substitute Peter Gain.
City snatched the lead in the 53rd minute when Yeo forced his way down the left flank and fired over a cross. Matthew Bloomer headed against the bar and when the ball came down Ciaran Toner prodded it in from close range.
Town keeper Kevin Pilkington then made a superb point blank save to keep out an effort from Green.
But Mansfield's chances of a point disappeared in the 65th minute when they were reduced to 10 men.
Central defender Luke Dimech wrestled Yeo to the ground as the Lincoln man tried to break clear from his own half. Referee Eddie Ilderton immediately red-carded the Town player for the foul.
Lincoln went on to waste a string of chances and when they did hit the target found Pilkington in excellent form.
The keeper made a superb save from Green when he pushed the ball away and then reacted quickly to complete the save as Gary Taylor-Fletcher moved in for the kill.
Richard Butcher wasted a glorious chance in the 71st minute when he shot straight at Pilkington.
Three minutes later Lincoln almost paid for their failure to find the net. A mistake by Gareth McAuley allowed Derek Asamoah to break down the right flank . The Town striker produced a perfect cross to find the unmarked Colin Larkin. The striker hit his shot well but Marriott produced an outstanding one-handed save.
Lincoln wasted another easy chance in the 76th minute when Taylor-Fletcher created the opening for Bloomer but the defender hit his shot into the stand.
Lincoln finally got their second goal of the game in the 82nd minute. Kevin Sandwith blasted in a 20 yard free-kick which came back off Pilkington. As the Town defenders watched, Yeo pounced for his 13th goal of the season.