The Robins have re-discovered their form since manager John Ward opted to rest some of his youngsters and select a more experienced side three games ago.
For Lincoln City, however, it was a tale of more defensive woe for a team that has now won only once in the last 10 league and cup games.
Both sides found life difficult in slippery conditions but it was Cheltenham who seemed to adapt better as the first half wore on.
They were given an early scare when Lincoln's new loan signing Richard Logan appeared unmarked at the far post but dragged his shot high and wide from a promising position.
Cheltenham goalkeeper Shane Higgs then held an audacious chip shot from distance by Lee Beevers, but the opening goal arrived with 31 minutes gone.
Lincoln defender Paul Morgan made a mess of trying to clear a long clearance from Higgs and Steve Guinan was able to collect the loose ball and beat Alan Marriott with an emphatic finish.
Higgs was called upon to make a superb save from Gary Birch shortly afterwards but he was powerless to stop the Red Imps from equalising on the hour mark.
Midfielder Nat Brown sent over a dipping cross from the right and defender Paul Mayo was on hand to score with a crisp finish at the far post.
Lincoln had been firmly on top at the start of the second half and Higgs was forced to make another fine save, this time from Luke Foster, but the match was decided in Cheltenham's favour with two goals in three minutes from exactly the same source on both occasions.
With 64 minutes gone Craig Armstrong supplied John Melligan down the right. His curling cross was met by Brian Wilson charging in at the far post and his firm header gave Marriott no chance.
The pair combined again moments later with Melligan displaying clever skill to get around Jamie McCombe and cross for Wilson to score with a low finish.
The scoring was completed in injury time when substitute Steven Gillespie ran on to a through pass from Grant McCann to score his first goal since arriving on loan from Bristol City.