Sean McConville and in-form Shay McCartan were the goal heroes as Stanley moved up to 13th place in the League Two table.
The Reds extended their unbeaten run to 11 games and closed the gap on the top seven to seven points with seven games to play.
Cambridge could have boosted their own top seven charge with a win but, missing ex-Stanley winger Piero Mingoia through injury and losing Blackburn loan defender Scott Wharton in the warm-up, the loss has hindered their promotion push.
Stanley’s first real chance fell to Omar Beckles on 10 minutes. The defender got on the end of McConville’s ball in but could only guide his header wide.
There were limited chances in rainy conditions but Stanley took the lead on 19 minutes when, after the ball bounced around the area, Jordan Clark set up McConville who fired it into the top of the net for his sixth of the season.
Cambridge almost replied immediately with Luke Berry heading Jake Carroll’s ball in narrowly wide.
McConville came close to his second on 22 minutes with a free header at the far post but he couldn’t get enough power on it and keeper Will Norris collected the ball.
A Leon Legge header on 28 minutes was bundled out of the six yard box by the Stanley defence and Berry had a close range strike blocked almost on the line as Cambridge looked for the equaliser.
On the stroke of half-time, United top scorer Berry had another chance but his header was well held by Aaron Chapman.
Stanley doubled their advantage on 55 minutes when Billy Kee played in the perfect pass to send McCartan racing free and the striker held his nerve to stroke the ball home for his eighth of the season – his fourth in three games
Stanley had to survive a few goalmouth scrambles but came close to a third on 67 minutes but no one could get a touch on McCartan’s ball which raced across the area.
McConville rifled narrowly over while McCartan blasted over as Stanley celebrated another important three points.