Centre half McEveley made it three on the hour, before Sammie Szmodics pulled one back.
The Blades regained their three goal advantage eleven minutes from time, thanks to a penalty by Baxter.
It was the U's first defeat on the road since November, and means they now sit four points from safety.Humes made one change to his starting line-up, bringing back Ben Gordon in place of Sanchez Watt on the left.
The U’s almost had the perfect start, with Sammie Szmodics having his first minute effort deflected onto the post and wide from Gavin Massey’s cross.
It proved an important save for the home keeper, with his side going ahead seven minutes later.
A free kick wide on the right was missed in the centre and found its way to Baxter at the far post.
His first touch took it close to Walker but the forward got a decisive toe and the hosts were ahead.
There was a good reaction from the U’s to the goal, with Tom Lapslie having two shots in quick succession.
The first came after a lung busting run from his own half and the second was a volley as a U’s corner was cleared to the edge of the box – both failed to test Turner in the home goal.
Chris Porter, returned to his former club, was then denied by a fantastic save by Turner after being found by a good through ball from Ben Gordon.
On the half hour, Alex Wynter put a header just over the bar, after Tom Eastman had headed a corner back into the danger area.
It was all U’s at this stage and David Fox got himself into a good position but shot weakly wide frm the edge of the box.
Szmodics then had a shot deflected for a corner, which came to nothing, as the U’s looked for what would have been a deserved equaliser.
Unfortunately, the next goal went to the home side and as well as being against the run of play, it was also very much on the break.
A U’s corner was headed clear and then a visionary volley by Harris found Matt Done breaking on his own into the U’s half.
He cut inside and curled a shot past Walker’s right hand and into the corner to double The Blades’ lead.
That came in the thirty seventh minute and turned out to be the final action of the first half.
The scoreline flattered the hosts but the U’s would have to be more clinical if they were going to get anything out of the game in the second period.
Tony Humes didn’t wait long before he made his first change, bringing on Dion Sembie-Ferris for Ben Gordon.
Sembie-Ferris went over to the right hand side, with Gavin Massey taking the place of Gordon on the left.
Done had the ball in the net on fifty four minutes, but Done had handled the ball before planting his shot into the bottom corner.
The Blades did get a third on the hour though, as McEveley drilled a shot in from distancwe after picking the ball up just inside the U’s half.
The U’s didn’t crumble though, and Sammie Szmodics got one back ten minutes later, clipping his shot past Turner and into the corner.
The three goal margin was restored with eleven minutes remaining though, as Matthew Briggs pulled down Coutts and Baxter scored from the resultant penalty.
Kenny McEvoy came off the bench for his U’s debut with two minutes to go, and almost made an immediate impact.
He was twice denied by a defender blocking shots, and the referee then called time on a game that went away from the U’s after a good start.
Another tough trip awaits the U’s at the weekend, with Oldham playing host to Humes squad.