City, despite being outplayed for most of the game, looked to be heading for extra-time against their Conference opponents, but in the first minute of stoppage time Gareth Seddon forced his way down the right flank and sent across to the far post.
Iyseden Christie escaped his marker and made no mistake from close range forcing the ball past City keeper Rob Burch.
The goal deservedly put Kettering into the second round. Lincoln struggled throughout the game only showing occasional glimpses of their best form.
The home team went close on 19 minutes when Dany N'Guessan beat three defenders inside the box, only for his shot to be pushed out by Lee Harper.
Kettering created the better chances with Chris Beardsley having a shot blocked by Daniel Hone. The ball came back to Craig Westcarr, but from a good position the midfielder blasted over.
Kettering should have gone ahead in the 37th minute when a superb pass from Andre Boucaud released Jean-Paul Marna. The winger left two defenders for dead but with the goal at his mercy fired against the post.
Kettering kept up the pressure after the break and missed another excellent chance when John Dempster headed wide from six yards.
Then a corner from Westcarr found the head of Exodus Geoghaghan but the big defender headed wide.
Lincoln went ahead in the 54th minute very much against the run of play. Stefan Oakes sent a free-kick deep into the Kettering area and N'Guessan headed back for Lenell John-Lewis to head in.
But that only spurred on Kettering to greater efforts and after a shot from Guy Branston was saved, they levelled in the 67th minute. Poor defending by Lincoln let in Westcarr, once on loan at the home club, and he drilled his shot past Burch for an easy goal.
Brett Solkhon then broke through only for Janos Kovacs to make an excellent tackle.
Then came Christie's winner to send the 600 visiting fans home happy.