Tom Shaw scored the only goal of the game as Cambridge took the three points at Lincoln.
A neat move involving Luke Berry saw Shaw slot past Joe Anyon for his seventh goal of the season.
U's goalkeeper Danny Naisbitt made fine saves from Jake Sheridan and Jamie Taylor, who also had a goal disallowed for offside.
Naisbitt also denied the hosts in injury time with a superb stop to deny Alan Power from 25 yards.
VIEWS FROM THE DRESSING ROOM
Lincoln City manager David Holdsworth told BBC Lincolnshire:
"We're all shocked how we never got anything out of it to be honest.
"These boys that have taken part tonight have been magnificent.
"I'm really proud of the boys and the way they've gone about it tonight because some of them are very stretched."