The Imps were second best for long periods but they kept their cool in front of goal to pick up an excellent three points in League Two.
After being under constant pressure for the opening 40 minutes, Lincoln opened the scoring on the break when Gary King found Ben Wright and the striker slotted home with style from an acute angle.
Paul Green made it 2-0 with his first goal for the Imps following an excellent run into the box and fine left-foot finish 20 minutes from time.
Shrimps striker Matty Blinkhorn was rewarded for his efforts three minutes into injury time when he pulled one back with a shot from close range.
Blinkhorn had come close on a number of occasions as Morecambe dominated for long periods, firing three efforts wide of the target and having one shot cleared off the line by Adie Moses.
Shrimps midfielder Craig Stanley also saw a shot cleared off the line by Gary Croft before the unfortunate Blinkhorn hit the post with a curler from the edge of the box.