Robins midfielder Josh Low got the vital breakthrough with a bullet header after 65 minutes. Lincoln had survived a warning a minute earlier when Junior Smikle somehow put the ball over the crossbar from just two yards out.
Danny Andrew wrapped up the victory with a superbly taken 25-yard free-kick two minutes from time to extend Lincoln's winless run to nine games.
Cheltenham nearly opened the scoring when Martin Riley headed a 14th-minute corner narrowly over. The visitors again went close when Theo Lewis got behind the Lincoln defence after 37 minutes but steered the ball wide.
Cheltenham goalkeeper Scott Brown was called on to make a rare save from another powerful Ali Fuesini shot, but the home side who had another let off just before half-time when they survived a penalty appeal when Riley went down under pressure from Tom Kilbey.
But the Robins were not to be denied victory and Low headed home David Bird's cross to put them in front. Then Andrew lashed home a free-kick from 25 yards to seal three precious points.
Source: PA
Source: PA