United’s spirited second-half fightback had looked set to give them the points at Tannadice, as two goals in three minutes from Nadir Ciftci and Andy Roberston put them ahead.
Those strikes cancelled out a 30th-minute opener from Motherwell's Henri Anier, but the visitors ensured a share of the spoils when Ainsworth fired home with 14 minutes left.
But the hosts were a completely different side after the break and equalised after 54 minutes when Ciftci found space on the left and ran unchallenged into the area, where he drilled a left-footed finish through the Lee Hollis' legs.
Three minutes later the game was turned on its head when Robertson was allowed to run 40 yards down the channel before sending a left-footed shot past the despairing dive of Hollis.
