Crawley scored twice in the second half to end a four-match losing streak and book their place in the second round of the JP Trophy.
Reds took the lead through an own goal from Richard Tait nine minutes after the break and wrapped up victory when Charles Banya came off the bench to score his first ever senior goal.
Crawley should have stretched their advantage as they took control after an unconvincing first half but Lewis Young was unable to make the most of a number of good chances.
Boss John Gregory made six changes to the side which lost 2-0 at MK Dons on Saturday including debuts for Jamie Ashdown and Mitch Rose.
Emmet O’Connor also came in for his full debut and could have marked the occasion with a couple of goals inside the opening 20 minutes.
The Canadian showed a lack of composure when he blasted well over from a good position early on and then saw the ball roll agonisingly wide of the post after poking a through-ball from Rose past the onrushing Chris Dunn.
There was no much else for a predictably low crowd to get excited about in the first half although Matt Harrold probably should have hit the target after being played in by a clever reverse pass from Gavin Tomlin while at the other end Robbie Simpson twice shot over from long-range.
Reds brought on Charles Banya for Rose at half-time and came out a completely different side.
Tomlin had the ball in the back of the net in the 51st minute when he ran in Lewis Young’s goalbound shot from an offside position.
More good work from Young almost brought the opener when his low cross hit a defender and deflected onto the far post.
Crawley’s pressure told soon after when Tomlin’s low centre slipped through the hands of Dunn and went in off the unfortunate Tait.
Reds should have doubled their lead when Young played in Jimmy Smith on the counter attack but the former Stevenage midfielder made a complete hash of the chance.
After a ten minute burst of excitment the game settled down into a familiar pattern although Crawley did look the more likely to extend their lead.
Young went close when he cut in from the left before shooting just wide before Banya came off the bench to fire a shot through the legs off Dunn following a nice one-two with Tomlin on the edge of the area.
It should have been 3-0 right at the end when Young shot wastefully over the bar with only the goalkeeper to beat.
Crawley (4-4-2): Ashdown; Oyebanjo, Leacock, Bradley, Dickson 6 (McLeod, 61); O’Connor, Smith, Rose 6 (Banya, 46), Young; Tomlin, Harrold 7 (Richefond, 71). Subs: Jensen, Isaacs.
Cambridge (4-4-2): Dunn; Tait, Coulson, Lennon, Taylor; Chadwick, Diallo, Champion (Hughes, 10), Donaldson; Stockley (Whittall, 60), Simpson (BJ Taylor, 90+4). Subs: Norris, Hurst.