The Imps wasted two early chances with Junior Mendes twice shooting wide after being left unmarked inside the box.
Mendes made amends in the 13th minute when his low cross from the right was turned in by Mark Stallard to give Lincoln the lead.
But City were then undone by poor defending. Four minutes later Lukas Jutkiewicz easily beat two defenders inside the box before firing the ball across the Lincoln goal. Christian Roberts was left unmarked at the far post and made no mistake from close in.
Lincoln had a let off in the 34th minute when both Jutkiewicz and Barry Corr mis-kicked in front of goal.
But seconds later, Town went in front when Michael Pook hammered the ball into the box and Corr fired home on his debut.
Lincoln went further behind four minutes into the second half when Corr turned his marker inside the six-yard box before setting up Lee Peacock for a tap in.
Lincoln had a let off in the 56th minute when a cross from Sofiane Zaaboub beat keeper Alan Marriott but came back off the bar.
Marriott was beaten again in the 72nd minute when Peacock smashed in a long-range free-kick but Lincoln were again saved by the woodwork.
City pulled a goal back in the 77th minute when new signing Peter Holmes set up Stallard, who scored his 15th goal of the season.
Lincoln desperately fought in vain for the equaliser with both Lee Frecklington and substitute Jamie Forrester going close in the final five minutes.