A fluke late goal condemned basement outfit Swansea City to their fourth consecutive defeat.
Brian Flynn's team held out despite being down to ten men from the 42nd minute but could do nothing about LincolnÂ’s winner.
Imps substitute Paul Smith blasted in a shot which beat Swans keeper Roger Freestone but came back off the post.
The ball ricocheted against the body of defender Kris O'Leary who could do nothing as it rebounded off him and rolled into the empty net.
The 89th minute goal was rough justice on the Welshmen, who created enough chances to have won comfortably.
Manager Flynn said afterwards: "It's always tough when you're playing with ten men, but we were hanging on for a result when we conceded a goal at the end. Even so there were a lot of positives to take from the game." Lincoln manager Keith Alexander added: "In the end it took a lucky goal but IÂ’m happy with that. We've played against ten men several times this season and not won." Swansea striker Marc Richards was denied twice in the opening three minutes by Lincoln keeper Alan Marriott as the Swans looked anything but a bottom of the league team.
Then Richards set up James Thomas but his low shot was blocked by the legs of Marriott.
Swansea kept up the pressure and Thomas left defender Paul Morgan trailing in his wake before setting up Richards. The striker had a great chance but once again Marriott was at his best to keep out the final shot.
Swansea suffered a blow three minutes before half time when Jamie Wood was red-carded for felling Red Imps winger Chris Cornelly on the halfway line.
Lincoln struggled to make the extra man count, but were unlucky on the hour when Simon Yeo hit a first-time shot narrowly wide.
Two minutes later Yeo was again left unmarked, but his shot came back off the post and the follow-up from Simon Weaver was blocked by Michael Howard.
Swansea continued to create chances and in stoppage time Richards had another clear-cut opening, but completely missed his kick in front of goal.