Manchester United will fight for a top-four finish in the Premier League until it is "mathematically impossible", says manager Jose Mourinho, after a 3-0 victory at bottom placed Sunderland.
In the day's other game Everton beat Leicester City 4-2.
Goals by Zlatan Ibrahimovic, Henrikh Mkhitaryan and Marcus Rashford eased United to a vital three points after drawing six of their previous nine Premier League games.
They are unbeaten in their last 21 league games but Mourinho's side, who moved above Arsenal into fifth place, are still four points behind Manchester City with a game in hand.
Liverpool, in third place, are six ahead of United having played two games more.
"We want to fight in the Premier League until it is mathematically impossible. The Premier League we cannot win, but Europa League we can," Mourinho said.
Romelu Lukaku scored twice as Everton defeated champions Leicester City 4-2 at Goodison Park in a game which saw four goals inside the opening 23 minutes.
Leicester, who face Atletico Madrid this week in the first leg of their Champions League quarter-final, made five changes ahead of their trip to Spain and the defeat ended the run of five straight wins since Craig Shakespeare replaced Claudio Ranieri as manager.
For Everton, it was a fine bounce back from their derby defeat to Liverpool and the disappointment of conceding an injury-time equaliser to Manchester United in their 1-1 draw last week.
Everton are seventh on the table and Leicester 11th.