The game looked all over 11 minutes after the break when Parkin was clumsily hauled to the ground by Gorkss, and Davidson made no mistake from the spot with a thunderous left-foot strike into the top corner.
United centre-back Nemanja Vidic appeared to be harshly punished for tugging at Frederic Piquionne's shirt as they went up for an O'Hara free-kick and Prince-Boateng, who missed a spot-kick last week, made no mistake this time.
Two minutes later, Accies were reduced to 10 men when Canning was sent off for denying McGowan a goal-scoring opportunity and Higdon made no mistake from the spot.
Wayne Rooney equalised after amistake by Ricardo Carvalho but Ballack struck the winner from the penalty spot after 86 minutes following a handball by Michael Carrick.
And Fabregas also played a hand in the second goal -- the former Arsenal midfielder earning a 56th minute penalty after being fouled by Domingo Cisma, with Messi making no mistake from the spot.