United, staring the Conference in the face, lost the game in the first half hour when Lincoln's domination brought them two goals.
The U's emerged in the second half looking a different team. They snuffed out the Lincoln attack but only managed to get one goal back.
Lincoln broke the deadlock in the 17th minute when Richard Butcher set up Simon Yeo and the striker hit a fierce left-foot shot into the net for his 16th league goal of the season.
Cambridge suffered a big blow in the 20th minute when striker Daniel Chillingworth pulled up with a hamstring injury and was stretchered off.
Yeo and Gary Taylor-Fletcher both went close before Lincoln doubled their lead in the 26th minute when midfielder Peter Gain sent over a cross from the left which Taylor-Fletcher converted with a left-foot volley.
Three minutes later Cambridge caught Lincoln on the break, but Shane Tudor flicked his shot just over.
Then a poor clearance from Jamie McCombe presented Tudor with another chance, but again he failed to hit the target.
Lincoln went close to a third goal in first-half stoppage time when Francis Green put Butcher in, but the midfielder's shot smashed against the bar.
Cambridge looked much improved after the break, fighting for every ball.
They got a goal back in the 53rd minute when an excellent pass from Matt Somner sent Tudor away down the right. The striker fired over a low cross which Daniel Webb slotted home from close range.
Cambridge keeper John Ruddy made two great late saves to keep his side in with a chance of salvaging something from the game.
And the U's almost snatched a draw in stoppage time, when Tudor was left unmarked inside the six-yard box, but his effort was saved by City keeper Alan Marriott.