The Red Imps came to Hull with a gameplan to get a goal and then defend it, but though they dominated the first half they will be rueing their failure to capitalise on their chances, allowing the Tigers to slowly get their confidence back.
Jason Price registered the first effort on goal, with a shot saved by Alan Marriott after five minutes.
But after 14 minutes, Richard Butcher had a shot cut out in the box as chaos reigned in City's penalty area.
Lincoln were frustrating City, pushing them deep, but there were no clear cut chances until the 25th minute when Paul Musselwhite flapped at Paul Mayo's corner, after which Butcher put a simple header over the bar.
Four minutes later Musselwhite produced an excellent fingertip save to keep out a shot from Gary Fletcher after Simon Yeo did well to put in a cross from the left.
On the half hour mark a good move by the Tigers saw Stuart Green shoot straight at Marriott, with Price's follow up hitting the sidenetting.
But right in the last minute of the half, totally against the run of play, Andy Holt put the Tigers one up after an excellent one two with Danny Allsopp.
After the re-start a dreadful defensive mistake by Simon Weaver was punished by Allsopp after 52 minutes.
Rory May and Mayo both saw efforts saved, before Stuart Green put the match beyond doubt ten minutes from time with a well-taken goal with Marriott in no-man's land, but City's three points were marred by crowd trouble in and outside the ground.