Lincoln City 0 Exeter City 1
A scruffy game looked to be heading for a goalless draw until Exeter's Dean Moxey fired a hopeful ball into the box from 30 yards.
His effort beat Lincoln keeper Rob Burch and struck the post before rolling into the net off the prostrate keeper's back.
The 88th-minute strike justified Exeter boss Paul Tisdale's decisions to push men forward for the final 20 minutes.
Until then Lincoln had looked the more likely team to break the deadlock.
The home team controlled the early part of the game going close after only 15 minutes when Exeter keeper Paul Jones was forced to block a low shot from Dany N'Guessan.
Lincoln kept up the pressure and, when Geoff Horsfield threatened, Grecians defender Rob Edwards deliberately punched the ball away on the edge of the box.
Edwards escaped without any sort of card and the resulting free-kick from Aaron Brown was deflected wide.
Jones made an excellent save in the 25th minute as Lincoln threatened again. Paul Green played the ball to 17-year-old Andy Hutchinson and the teenager produced a first-time shot which Jones did well to push away.
Exeter, with the breeze behind them, stepped up their game in the second half and Craig McAllister was unlucky in the 64th minute when he fired in a shot through a crowd of players only for Scott Kerr to clear off the line.
Exeter brought on Richard Logan for the final 20 minutes as they switched to a three-man strikeforce.
Almost immediately they threatened when Stuart Fleetwood was put clear but the striker lobbed his shot over the top.
At the other end Lincoln sub Nathan Adams, another 17-year-old, was only denied a goal by a superb 73rd-minute save from Jones.
But with time running out Exeter grabbed their freak goal to keep them in the hunt for automatic promotion.