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."
Live Text Commentary
Jefferson Louis takes a inswinging corner.90:00 +2:45 Full time
Full Time The game is over, as the referee blows his whistle.90:00 +1:24
Alan Power takes a shot. Danny Naisbitt makes a save.90:00 +0:36
The assistant referee signals for offside against Michael Gash. Joe Anyon takes the free kick.89:23
The referee blows for offside against Francis Laurent. Direct free kick taken by Danny Naisbitt.87:01
Corner from the right by-line taken by Alan Power, Header on goal by Josh Gowling from inside the box goes harmlessly over the target.84:41 Substitution
Substitution (Cambridge Utd) makes a substitution, with Jack Eades coming on for Liam Hughes.81:08 Substitution
Substitution Michael Gash comes on in place of Andy Pugh.80:31
Effort from outside the area by Alan Power goes wide right of the goal.75:55 Substitution
Substitution Nialle Rodney joins the action as a substitute, replacing Jake Sheridan.72:46
John Nutter fires a strike on goal direct from the free kick.72:46 Booking
Booking Blaine Hudson is shown a yellow card for unsporting behaviour.72:25
Free kick awarded for a foul by Blaine Hudson on Danny Lloyd.71:38
Jefferson Louis takes a shot. Save made by Danny Naisbitt.70:34
Free kick awarded for a foul by Luke Berry on Francis Laurent. Free kick taken by Tyrone Thompson.69:33
Alan Power takes a inswinging corner.68:59
John Nutter takes the inswinging corner, Josh Gowling takes a shot. Danny Naisbitt makes a save.67:36
Inswinging corner taken right-footed by Jake Sheridan from the right by-line, Unfair challenge on Rory McAuley by Tom Miller results in a free kick. Danny Naisbitt restarts play with the free kick.66:15
Unfair challenge on Francis Laurent by James Jennings results in a free kick. Free kick taken by John Nutter.64:15
Danny Lloyd produces a right-footed shot from the edge of the area and misses to the left of the goal.
Substitution Francis Laurent on for Jamie Taylor.56:39 Substitution
Substitution Danny Lloyd on for Nicky Nicolau.54:15
Jamie Taylor challenges Kevin Roberts unfairly and gives away a free kick. Danny Naisbitt takes the free kick.47:00 Goal scored
Goal! - Tom Shaw - Lincoln 0 - 1 Cambridge Tom Shaw finds the net with a goal from inside the area to the bottom right corner of the goal. Lincoln City 0-1 Cambridge Utd.45:01
The referee gets the second half started.45:01 Substitution
Substitution Blaine Hudson on for Michael Wylde.45:00 +1:11 Half time
Half Time The whistle is blown to end the first half.43:29
Corner from left by-line taken by Rossi Jarvis.43:13
Corner taken by Rossi Jarvis, clearance by Tom Miller.42:26
Corner taken by Rossi Jarvis, clearance made by Paul Robson.37:12
Unfair challenge on Tyrone Thompson by Tom Shaw results in a free kick. Direct free kick taken by Paul Robson.33:27
Jefferson Louis challenges Michael Wylde unfairly and gives away a free kick. Free kick taken by Luke Berry.29:32
The referee blows for offside against Jake Sheridan. Danny Naisbitt restarts play with the free kick.22:37
The assistant referee flags for offside against Josh Gowling. Indirect free kick taken by Danny Naisbitt.21:39
Free kick awarded for a foul by Tyrone Thompson on Rossi Jarvis. Danny Naisbitt takes the free kick.20:42
Liam Hughes has an effort at goal from deep inside the area missing to the left of the target.20:24
Luke Berry takes a shot. Paul Robson gets a block in.12:53
Jamie Taylor takes a shot. Save by Danny Naisbitt.12:41
Foul by Jamie Taylor on Michael Wylde, free kick awarded. Direct free kick taken by Danny Naisbitt.11:57
Jake Sheridan challenges Tom Shaw unfairly and gives away a free kick. Direct free kick taken by Danny Naisbitt.10:30
The offside flag is raised against Jefferson Louis. Free kick taken by Danny Naisbitt.9:40
Shot from inside the six-yard box by Jamie Taylor goes wide right of the target.7:24
The assistant referee signals for offside against Jamie Taylor. Indirect free kick taken by Danny Naisbitt.1:41
The assistant referee flags for offside against Jamie Taylor. Danny Naisbitt takes the direct free kick.0:19
Jake Sheridan takes a shot. Save by Danny Naisbitt.0:00
The referee gets the match started.
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