But the win was marred by a serious injury to young centre-half Adam Davies, who had to be taken to hospital with breathing difficulties after getting a kick in the throat.
While the Wales Under-19s captain received extensive treatment on the pitch the Conference match was held up for 21 minutes, with the players at one stage returning to the changing rooms.
Davies was hurt in a 58th minute collision with Exeter's Jamie Mackie and after falling heavily complained he was having trouble breathing. He was taken to Addenbrookes Hospital for treatment.
Cambridge were leading 1-0 at that stage following a strange 14th minute goal when a cross from Jon Brady slammed into the boot of striker Fola Onibuje, the ball looping up to be headed into the net by the lanky forward.
Exeter tried hard for the equaliser, coming close a couple of times through Chris Todd and Andy Taylor before the break.
And when they drew level 14 minutes after the long delay for the injury, it seemed they might go on to get the victory they needed to boost their play-off hopes.
Lee Phillips who had hit the post in the 61st minute, was more accurate in the 72nd when he chested the ball into the net from Dean Moxey's cross.
With Cambridge missing their other centre-back Mark Peters as well as Davies, also due to injury, Exeter looked favourites for a win, but they were let down by over-enthusiasm.
Pushing up ten minutes from time they left a gap which Cambridge exploited brilliantly.
Brady slotted a long ball through the middle and loanee Jamie Guy slipped inside Danny Woodards, ran on and beat the advancing keeper to hit the winner.