Tom Craddock's late winner left Lincoln needing a win on the final day of the season to secure League Two safety after defeat to Oxford.
Craddock fired in from 14 yards, after Asa Hall had volleyed in a corner to equalise for the hosts.
Cian Hughton had given Lincoln a dream start when he headed in Gavin McCallum's left-wing cross.
Daniel Hone saw red late on for Lincoln when he picked up a second yellow following a foul on James Constable.
Lincoln City manager Steve Tilson told BBC Lincolnshire:
"We went 1-0 up and were really comfortable but we needed a second goal just to give ourselves a bit of a breathing space but things aren't going our way.
"Winning becomes a habit and losing becomes a habit, and it's only us that can get ourselves out of that habit and we have to now go and win on Saturday.
"The pressure's there and the players have got to deal with it. We can say the right things to try and take the pressure off, but at the end of the day they've got to perform on the pitch."