Lincoln moved to just two points outside the League Two drop zone after defeat by fellow strugglers Cheltenham.
Ali Fusseini and Ben Hutchinson both went close as the hosts started brightly before the Robins began to dominate proceedings.
The visitors deservedly went in front through Josh Low's bullet header from David Bird's centre.
Danny Andrew sealed all three points late on when he smashed home a free-kick from 25 yards.
The Imps are now just two points clear of Barnet in the final relegation place.
For Cheltenham the victory means they require just one point from the last two games to ensure their league status.
Lincoln City midfielder Luke Howell told BBC Lincolnshire:
"It's not nice in the changing room when you go in after a result like that but we've only got ourselves to blame.
"It seems that if we don't get the first goal, the longer it stays 0-0 the less confident we get and the less want the ball, but we're footballers, you have to want the ball and do your bit for the team. If not, there's not much point being on the pitch.
"I don't know whether we're afraid to make a mistake or whether it's the pressure of relegation because some players haven't had this before. I felt we were on top for the first 40 minutes but when the goal went in you could see the whole team just deflated."