City found it difficult to get into the game against a Robins team that was well-organised with five men across the middle.
But when the chances came City's way their strikers failed to hit the target and Cheltenham took the points thanks to a late winner.
Lincoln, without five first-choice players, looked lively at the start with Richard Butcher. back on loan, firing in a 20-yard shot that Cheltenham keeper Shane Higgs saved.
Then Gary Birch forced his way down the right flank but his cross was cut out by the Cheltenham keeper.
Town hit back in the 25th minute when David Bird found the head of Damien Spencer but his effort went straight at City keeper Simon Rayner.
Then in the 43rd minute John Melligan broke clear and sent over a deep cross. Adam Connolly was first to react but his shot was saved by Rayner.
Lincoln pinned Cheltenham in their own half for a 20 -minute spell but Town held out.
Teenager Oliver Ryan twice went close and Scott Kerr almost snatched a goal with an inswinging corner but Higgs pushed his effort out.
Cheltenham grabbed the winner in the 76th minute after Lincoln sub Jeff Hughes brought down Melligan. The Lincoln man was booked and then Grant McCann fired the free -kick into the box for Kayode Odejayi to head in.
Lincoln almost equalised three minutes later when Cheltenham defender Shane Duff left a long ball for his keeper but Derek Asamoah nipped in between them only to hit his shot straight at Higgs' body.
Francis Green almost scored in the closing minutes but Cheltenham could have added to their lead in stoppage time. Odejayi almost got on the end of a Melligan cross and then seconds before the whistle the Cheltenham striker broke away again but his lob was saved by Rayner.