The result put the Dons level with Peterborough at the top of League Two, but they must have been disappointed with the way they allowed Lincoln back into the game.
The Dons also suffered a double blow with centre-back Sean O'Hanlon and midfielder Colin Cameron both forced off with injuries in the first 50 minutes.
Lincoln struggled early on and went a goal behind after only three minutes when Lloyd Dyer saw his shot blocked, but Carl Regan followed up to fire in from six yards.
The Dons then stayed in control without really threatening the Lincoln goal and when City ventured forward they found it difficult to create chances of their own.
O'Hanlon went down in the 16th minute holding his face and, after lengthy treatment on the pitch, was eventually led off with the visitors having to reshuffle their back four.
Paul Ince's side suffered another blow early in the second half when Cameron was caught by a heavy challenge from Gary Croft and limped off with a knee injury.
Skipper Keith Andrews almost grabbed a second goal in the 48th minute when he fired a free-kick over the Lincoln wall only to be denied by a diving save from Alan Marriott.
Six minutes later, Dyer beat the home side's offside trap and broke away, but sent his shot straight at the Lincoln keeper.
Marriott was left helpless though in the 55th minute when Jemal Johnson turned on the edge of the box and fired a left-foot shot into the bottom corner.
Lincoln got back into the game on the hour after some sustained pressure.
A header from Lee Beevers was pushed out by Willy Gueret, but Ben Wright followed up to hit the bar before forcing the rebound into the net.
Lincoln should have levelled five minutes later when the Dons defence failed to deal with a free-kick from Croft.
The ball came to Danny N'Guessan on the edge of the six-yard box, but despite having a free header, he sent his effort straight at Gueret.