Wayne Gray's penalty on the stroke of half-time gave the doomed ex-Londoners a shock half-time lead, but namesake Andy struck twice in the second period to end a run of three successive defeats for the Blades with a 2-1 win.
The fired-up Blades went straight on the offensive with Simon Francis testing Wimbledon goalkeeper Scott Bevan with an overhead kick in the fifth minute.
Wimbledon then reminded the Bramall Lane faithful they are more than capable of taking another big scalp - following away wins at West Brom and more recently at Wigan - when Wayne Gray flashed a shot narrowly wide from 25 yards.
United swarmed forward though and Bevan did well to punch clear Nick Montgomery's dangerous cross, while Robert Kozluk fired wide from the edge of the penalty area.
Bevan held Jack Lester's header from a Francis cross, but the Londoners, criticised by boss Stuart Murdoch for feeling sorry for themselves at Preston, showed none of the same signs here.
The Dons goalkeeper clung on to Alan Wright's curling free-kick, but Gary Smith forced Paddy Kenny into a smart save with another long-range effort and the home keeper was at his best to deny Wade Small from six yards before Malvin Kamara blazed over.
Montgomery saw his shot blocked and Blades defender Chris Morgan headed wide before United were made to pay just before the interval. Kamara had just seen his shot blocked by Morgan and when the same player went clean through on goal only to be brought down in the box by Kenny, Gray smashed the ball home from the spot.
But the Blades were back on terms five minutes after the restart. Alan Wright swung in a near-post corner and Andy Gray headed home his fifth goal in 10 games for United since arriving from Bradford.
Kamara and Small were both booked for dissent immediately after and only the woodwork denied Gray from the edge of the box as United swept forward.
Blades fans were then celebrating when Nico Herzig brought down Lester in the penalty area, but cheers were short-lived as the former Nottingham Forest striker pulled his spot-kick wide.
It was end-to-end action, with Small once again testing Kenny from 20 yards and Wright's bullet from similar distance blocked by Harry Ntimban-Zeh.
Gray dragged a close-range shot wide and Smith and Jermaine Darlington peppered Kenny with 20-yarders.
But it was United who made the breakthrough with Gray pouncing again to lash the ball high into the net from close range following Michael Tonge's free-kick.
Home fans' hearts then missed a beat as Small powered in another 20-yard shot but Kenny made another fine save to keep his side's promotion hopes alive.