It was Zlatan Ibrahimovic who opened the scoring in the first half with a neat turn and finish before Sebastian Larsson got sent off for a reckless challenge on Ander Herrera.
"But the game is improving, I am getting better and better and like I said, I feel like Benjamin Button - I was born old and I will die young!"
He got his name on the scoresheet again in more prosaic circumstances just 46 seconds after the restart.
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Zlatan Ibrahimovic needs more support from players like Jesse Lingard at Manchester United.
Manchester United kept pace with its UEFA Champions League qualification rivals as it pushed 10-man Sunderland closer to relegation from the English Premier League with a 3-0 victory yesterday.
Mourinho embraced Shaw and appeared to give him words of encouragement after replacing him with Daley Blind just past the hour mark, and the Portuguese said afterwards that the ex-Southampton man played well.
Injuries to Phil Jones and Chris Smalling leave Mourinho mean Shaw is likely to feature in a big week for United, with the trip to Anderlecht for Thursday's Europa League quarter final followed by Chelsea's arrival at Old Trafford on Sunday.
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Television replays suggested Pawson's decision was harsh and boss Moyes said: 'I don't want to make you think it's the referee's fault, it's not that.
"What I don't want to do is in any way blame the referees because our position is where we are, we are bottom of the league, so let me make that clear first of all, it's nothing to do with referees".
"He has a problem with his hip", Mourinho told BBC Sport.
It was Pochettino who helped to develop him when the pair were together at the Saints between 2013 and 2014 and subsequently earned seven caps for England. In away games we have to do the same.
After a good early spell from the visitors though the home side came more into the game with Lee Cattermole forcing a save from Romero from outside the box.
With his United contract due to expire in June 2018, however, Shaw is not blessed with time to prove his manager wrong. "When you play against a team that is sad, if you score before [them], the game is nearly over because it is hard to react".
David Moyes says Seb Larsson's red card changed the course of today's game against Manchester United - but refused to use it as an excuse for another Sunderland defeat.