The 90th minute strike was the only goal in a game which seemed destined for stalemate.
Reds boss Sir Alex Ferguson told Setanta Sports, "It was a little break that we got with it coming off the post and Nemanja fortunately was there.
"We decided in the last few minutes to just keep him up the pitch, because the way they were playing â€“ there was no threat from them.
"So we decided to play Rio on his own at the back and push the others forward and it paid its dividends - the little break made it all worth it."
Ferguson understood the reasons for Sunderland setting out their defensive stall.
"It was difficult because there were no spaces," he said. "They basically had ten men strong across the penalty box.
"Itâ€™s understandable when youâ€™re down the bottom of the league and you come to Old Trafford, there have been better teams who have come and been just the same."