It was goalless at half time but that was due to the brilliance of United's 18-year-old goalkeeper John Ruddy. He saved a succession of goal bound shots, several of them with his feet.
Ruddy was quickly into the action when Kevin Gall broke through in the 10th minute. Gall's shot was on target but the tall youngster got his feet in the way to prevent what looked a certain goal.
United's attacks were few and far between but in the 22nd minute they might have snatched the lead when Stephen Reed, making his first start of the season for Yeovil, gave the ball away and Daniel Chillingworth chipped goalkeeper Chris Weale only for his shot to go wide.
Yeovil were quickly back on the attack. In the 25th minute Ruddy tipped over a good sot from Bartosz Tarachulski and seven minutes later, when Phil Jevons put Andrejs Stolcers clear, the Latvian international had his shot saved by the keeper's feet.
The half finished in similar vein with Paul Terry having a shot brilliantly tipped round the post by Ruddy and Jevons narrowly off target with one that did beat the keeper.
Yeovil got the breakthrough they needed after 60 seconds of the second half.
A corner on the left was headed against the bar by Scott Guyett and Terry scrambled in the rebound.
Cambridge then came out of their defensive shell and claimed a deserved 78th minute equaliser.
Substitute Darren Quinton robbed Darren Way to set up Shane Tudor who rounded the keeper to score.
Yeovil's manager Gary Johnson sent on speedy substitute Yemi Odubade in the 84th minute and it proved the masterstroke.
His speed took him clear into the box where he was brought down by Ruddy for a clear penalty which Jevons dispatched for his 20th goal of a prolific season.