Constable’s neat left-footed finish, his ninth goal of the season, and Hall’s header put the U’s two goals ahead at the break, leaving the Dons without a league win since October 8.
The visitors started brightly and Tom Craddock blazed two good chances over, before Constable broke the deadlock on 17 minutes.
AFC Wimbledon threatened a response but Sammy Moore’s 20-yard effort was off target before Hall’s simple header doubled Oxford’s advantage and knocked the wind out of the hosts’ sails.
The Dons roared back in the second half and substitute Ricky Wellard played in Rashid Yussuff who smashed the ball against the underside of the bar. But the Us continued to threaten at the other end with Craddock forcing an excellent save from Seb Brown before firing wide of goal.
Anthony Tonkin then arrived at the back post but his missed the target, mere moments before Alfie Potter unleashed a terrific strike that went just over the crossbar as Oxford ran out comfortable winners.