Jose Mourinho vowed to take Manchester United's fight for a top-four finish to the wire as Luke Shaw found himself back in the manager's good books.
United reduced the gap to fourth-placed Manchester City to four points, with a game in hand, after a 3-0 victory at 10-man Sunderland, a result which pushed the Black Cats to the brink of relegation from the Premier League.
Mourinho, who takes his side to Anderlecht for the first leg of their Europa League quarter-final on Thursday evening, was a happy man after seeing them cruise to victory at the Stadium of Light.
He said: "After Liverpool and Manchester City's victories, if we didn't win today it's almost mathematically impossible (to finish fourth).
"It was important for us to win and that was the main objective.
"We did that and, apart from that, there were no more injuries to add to the difficult list we have, because we don't hide that we are still fighting for our situation in the Premier League.
"But the Europa League becomes fundamental for us, it's the only competition we can win now.
"We did the Community Shield, we did the League Cup. The Premier League, no way, so it is our competition to fight for."
Victory on Wearside was secured by Zlatan Ibrahimovic's stunning 30th-minute strike and, after Sebastian Larsson had been controversially dismissed by referee Craig Pawson for a challenge on Ander Herrera, second-half goals from Henrikh Mkhitaryan and substitute Marcus Rashford.
But it was full-back Shaw, criticised roundly by Mourinho in recent weeks, who earned a pat on the back from the Portuguese following a composed display.
He was taken off just after the hour following an early caution.
He said: "He played well, played solid. The opposition was not creating big problems, but he was solid and was confident with the ball.
"He was going forward with some danger, he was reading the game well to go when Mkhitaryan went inside. He played really well, so it was a good hour for him.
"I thought about a half-time change, but thought it was too harsh for him.
"I wanted him to play a little bit more, so at 2-0, one hour in, with the crowd asking for everything and putting the referee under a little bit of pressure, no risk (taken).
"We have no players, we need him to be available for the next match."
It proved to be another bleak afternoon for former United boss David Moyes, whose side remain 10 points adrift of safety with just seven games remaining.
Sunderland will consider an appeal against Larsson's dismissal with the Scot convinced his midfielder was harshly treated.
Moyes said: "We'll have a look at it. I've had a look at it, so don't worry about that, I've had a look at it.
"I don't want to make you think it's the referee's fault, it's not that. But he gets the ball, he touches the ball. There's no contact at all, so it's not even a booking.
"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.
"But I didn't think it was a good decision."
The Black Cats look doomed, but Moyes is refusing to admit defeat.
Asked about their situation, he said: "It's still as difficult - probably more difficult because there's a game less. The game less means it's tougher.
"There's no hiding the fact that we're in a difficult position. But we've got a home game next, let's see if we can get some momentum, try to get a win in that and we'll try to do that."