The Red Imps, desperate for a win to keep their play-off hopes alive, just about deserved their victory after holding out against strong Hull pressure.
But the defeat was a big blow to the Tigers who are now five points behind division three leaders Doncaster Rovers.
Lincoln started brightly and went close in the tenth minute when Peter Gain was denied by a diving save from Hull keeper Boaz Myhill.
Stuart Green hammered a shot wide before Hull wasted a great chance to go in front two minutes before the half-time break.
Junior Lewis, reunited with his former boss Peter Taylor after signing from Leicester in midweek, slipped a great pass to Ben Burgess.
But with the goal in front of him the big striker blasted his shot against the crossbar.
Hull had a let-off early in the second half when skipper Marc Joseph made a goal-line clearance to keep out a header from Marcus Richardson.
Then Myhill produced an excellent save to keep out a goal-bound header from Ben Futcher.
Stuart Elliott and substitute Jamie Forrester both wasted chances for the Tigers before Lincoln hit them with a set-piece move.
A long throw from Gary Fletcher was only half-cleared and Gain hooked the ball back into the net.
Hull had the chance to equalise two minutes later but Marriot made a superb save from Elliott.
But Lincoln pulled away to add a second goal five minutes from the end. Richard Liburd crossed from the left and Paul Mayo bundled the ball into the net.
Afterwards Lincoln manager Keith Alexander said: "The lads worked hard and gave a good performance.
"We weathered the storm and in the end got our just desserts. I always thought that if we kept going we'd get a goal."
Hull manager Peter Taylor said "We were absolutely outstanding in the second half.
"The only disappointing thing was that we didn't score. We missed some good chances and we had a bit of bad luck."