The Blades, with one eye on Sunday's FA Cup semi-final clash against Arsenal, made seven changes from the side that drew 2-2 with Crystal Palace.
Michael Tonge and Saturday's goal hero Steve Kabba were among the substitutes as Neil Warnock took a gamble on his fringe players, and his plan failed as Shipperley pounced to net the only goal of the game in the 38th minute.
The visitors threw everything at Wimbledon in the second half but failed to find a way through, even when Adam Nowland was sent off with seven minutes remaining.
The Dons took the lead against the run of play. Patrick Agyemang's driving run into the area ended with a fierce shot that was spilled by goalkeeper Paddy Kenny, and Shipperley was first to react to poke home the rebound.
The Blades responded and had the ball in the net minutes later. Owen Morrison beat three defenders before slipping the ball through to striker Dean Windass. He slammed the ball home but the referee had already whistled for offside and the home side escaped.
Windass was agonisingly close again in first half injury time as his free-kick cleared the wall but clipped off the top of the crossbar.
Darren Holloway's late challenge on Ben Doane after 56 minutes left the Blades youngster in a heap and, after treatment, Tonge came on as the defender was taken away in an ambulance.
United were enjoying a lot of possession without creating too much, but Paul Peschisolido spurned a golden opportunity in the 74th minute. Shaun Murphy lofted the ball over the top, leaving the Canadian one-on-one with Davis. His neat lob beat the Dons stopper but the ball also cleared the crossbar.
Nowland was booked for a challenge on Morrison after 81 minutes, and two minutes later was given his marching orders after bringing down Peschisolido. Warnock threw on Carl Asaba and Peter Ndlovu in a desperate attempt to snatch an equaliser, but the Dons held on.
Man of the Match: Owen Morrison