Manchester United put a spate of recent draws behind them with a routine 3-0 win at bottom club Sunderland, while Romelu Lukaku scored twice as Everton defeated champions Leicester City 4-2 at Goodison.
United are in sixth place in the Premier League table, seven points off the top four, but can move ahead of Arsenal into fifth if they avoid defeat at the Stadium of Light.
A hugely controversial moment then came two minutes before the break when Black Cats midfielder Sebastian Larsson was shown a straight red card for a challenge on Ander Herrera.
Speaking to Sky Sports after the game Ibrahimovic said that his age was not a concern and that he feels younger as he gets older.
Moyes said: "We'll have a look at it".
Sunderland face West Ham United at the Stadium of Light on Saturday and Moyes insisted he can not ask for more from his players despite the team having won only one match since December.
Henrikh Mkhitaryan netted United's second from the restart without Sunderland even touching the ball, and Marcus Rashford wrapped things up late on in a match in which United never had to get out of second gear.
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Ibrahimovic's goal woke up United, as Mourinho's lads raised the tempo and started to predominate the goal.
Despite Defoe wasting another chance for Sunderland late on, United were able to see out the remainder of the game easily, with substitute Rashford adding a third in the 90th minute, drilling the ball into the bottom corner after being teed up by Ibrahimovic.
"But when you play against 10 and the team is losing you find more spaces and normally you kill matches".
He said: "We reacted to the results of yesterday". Today was a good win and we have to keep working, keep believing we can reach the top four. "Afterwards we play with one more, sometimes it can be more hard and sometimes it can be an advantage".
It's not clear whether Mourinho is going to make the Premier League or Europa League his top priority, but he does still have to think about both ... all because of one result.
United-who started with Sergio Romero in place of goalkeeper David De Gea because of an unspecified problem-controlled the opening exchanges and had plenty of possession in the hosts' half without particularly threatening.
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