Casemiro's spectacular first-half goal proved decisive as Manchester United won 1-0 away to Bournemouth on Saturday to move within sight of Champions League qualification.
Erik ten Hag's side would have been assured of a place among Europe's elite next season had Liverpool lost to Aston Villa but their arch-rivals came from behind to secure a 1-1 draw.
Even so United now need just one point from their remaining two Premier League games this season - with the London duo of Chelsea and Fulham visiting Old Trafford on Thursday and a week on Sunday respectively - to be assured of a Champions League place.
That would mean Ten Hag had achieved his key target in his first season in charge, with United having already won the League Cup ahead of next month's FA Cup final against local rivals Manchester City at Wembley.
Marcus Rashford missed out for three-times European champions United with an unspecified illness, the England forward having also been sidelined from last week's 2-0 win over Wolves due to a leg injury.
But despite his absence, United took just nine minutes to go ahead on the south coast.
Christian Eriksen's floated cross into the box was flicked into the path of Casemiro by defender Marcos Senesi before the Brazilian midfielder hooked in an acrobatic volley.
Dominic Solanke, however, could have equalised for Bournemouth but his low drive was well-saved by David de Gea.
Casemiro then tried to top his goal with a thumping drive from 35 yards that Neto did well to hold.
Solanke too went close when he headed just over the crossbar in the last action of the first half.
David Brooks, making his first start since being diagnosed with cancer in 2021, almost levelled after the interval only for De Gea to turn his fierce drive over the bar.
United, however, continued to push for a second goal against a Bournemouth side who had fought so hard to be assured of top-flight safety long before this match kicked-off.
Bournemouth's Illya Zabarnyi prevented United from extending their lead when the Ukrainian turned Bruno Fernandes's first-time effort over the bar.
Fernandes's powerful shot stung the palms of Neto before Bournemouth squandered a chance to equalise when substitute Kieffer Moore, with only De Gea to beat, shot straight at the keeper, who saved with his leg.
Bournemouth weren't finished, with Senesi volleying on to the roof of the net in added time before United made sure of victory.