After the break, the Blades got two back, through Sharp and Woolford but Marvin Sordell struck late to make it 3-2.
Having already seen his save from a Sharp penalty overruled and been beaten by the retake, Jamie Jones then saved a late penalty to preserve the lead and the whistle went after six minutes of added time, giving the U's a vital win.
Tony Humes made one change to his starting eleven, with George Moncur coming in for the injured Alex Gilbey.
From the start, neutrals would have been hard pressed to guess which team were at home, with the U’s dominating possession in the early stages.
Tom Eastman did have to be alert from a breakaway attack, but he was on hand to head over when a far post cross came in on four minutes.
Two minutes later and the U’s got the opener, with George Moncur scoring for the second time in three days.
He linked up superbly with Marvin Sordell and when the return pass came in, Moncur’s first touch was perfect for him to drill a low shot past the exposed Howard.
Billy Sharp tried to respond for the hosts but put his header too close to Jamie Jones when a cross came in from the Blades’ right.
The U’s were closing Sheffield players down extremely quickly, forcing errors and this allowed the likes of Massey, Harriott and Sordell to break at pace from good positions.
In the fifteenth minute, two of the three combined and Harriott had a shot saved from Massey’s crossfield pass.
The pressure told and halfway through the first period, the U’s doubled their lead.
It was a double for Moncur, as he darted onto a superb reverse pass from Gavan to once again drill a low shot past Howard, this time to the keeper’s left.
Moncur then put a curler just the wrong side of the upright, as the U’s looked for more goals against a stunned Blades’ defence.
Owen Garvan was next, his free kick was tipped round the post with Howard at full stretch to prevent a third U’s goal.
Massey then shot wide after another good move, before Joe Edwards grazed the bar with a twenty yard effort.
The crowd had already started to get on the Blades’ backs and that spurred them on to get forward more in the last few minutes of the first half.
Sharp twice and Woolford had opportunities but Jones was on hand for two efforts and Sharp blazed the third over the bar.
The whistle went with the U’s leading 2-0 and being very good value for that lead.
Unfortunately, that lead didn’t remain at two for long, with the hosts getting a goal back within four minutes of the restart.
Massey was harshly adjudged to have fouled McEveley as he drove into the box and Billy Sharp stepped up to take the spot kick.
Jamie Jones saved diving to his right but the officials decided that he had moved forward before the kick was taken.
Sharp kept his nerve and put the retake the other way to make it 2-1.
The goal boosted the Blades and it was almost level on fifty seven minutes but after doing all the hard work with a jinking run, McNulty poked his shot wide.
Sharp then should have also scored but Jones stayed on his feet just long enough to force the striker wide and the shot was put wide from an angle.
Just after the hour, the equaliser did come, with Woolford getting onto the ball first in the box and sliding a shot low past Jones.
At this stage, many observers would have been thinking the hosts were favourites to go on and win but the U’s didn’t read that script.
Garvan was again denied by a save from a free kick and then Sordell and Massey were denied by good defending.
The ball wasn’t cleared from that chance and Garvan had the third effort in twenty seconds, volleying his shot narrowly wide.
Moncur had another free kick blocked but the U’s weren’t to be denied a third.
Sordell took control of the ball from a Moncur pass and drove inside from the left and shot from just outside the box.
The keeper looked like he had it covered but a wicked deflection took the ball past him and into the back of the net.
Four minutes later, the home team got a chance to level things up again, as Elokobi got caught wrong side of Sharp and bought down the lively Blades’ striker.
A red card was issued to the U’s defender and Sharp stepped up for another penalty.
Jones dived to his right, waiting until the kick was taken, and parried away the spot kick to preserve the lead.
Frankie Kent had come on for Moncur before the penalty was taken and the youngster helped his side repel any further attack.
After an agonising six minutes of added time, the referee blew the final whistle and the U’s had deservedly won their first game of the season.
The three points took the U’s out of the bottom four and gave them a big boost ahead of the table toppers Gillingham’s visit to the Weston Homes Community Stadium on Saturday.