- Casemiro (9')
United moved on to 69 points in fourth place in the table, behind Newcastle United on goal difference and needing one point from home games against Chelsea and Fulham next week to seal a return to European club soccer's most prestigious competition.
The visitors dominated the opening exchanges and went ahead in the ninth minute when Cherries defender Marcos Senesi tried to hook away a Christian Eriksen pass behind the defence, but only succeeded in teeing up Casemiro for a brilliant spinning volley.
The home side found their feet midway through the first half as Dominic Solanke controlled a long ball into the box and unleashed a shot that David De Gea had to dive to his left to save.
That sparked a positive spell for Bournemouth, with Victor Lindelof forced into a number of defensive headers, but they were soon on the back foot again as United took control again in the second half.
Winger Antony wasted a number of decent chances, while substitute Wout Weghorst and midfielder Bruno Fernandes both forced fine saves from Neto and it looked like it was only a matter of time before United scored again.
They were almost made to pay for their wayward finishing when substitute Kieffer Moore bore down on De Gea late on, but the goalkeeper blocked his shot and the danger was averted.
There was still time for one more chance for the home side, with Senesi firing just over the bar, but United held on for a win that prompted wild celebrations from the travelling supporters.
"The only criticism is we didn't kill off the game, we had to produce that second goal but that's the way this team are. It is not easy scoring goals," United manager Erik ten Hag told the BBC.
As Manchester United's game was ending, Liverpool were a goal down to Aston Villa and a defeat there would have guaranteed United's qualification for the Champions League. But even though Roberto Firmino equalised for Liverpool, Ten Hag said he was not interested in that result.
"I don't care what happens in Liverpool, it's about us. We have to do the job," he said.
- Chris Kavanagh
|Brighton & Hove Albion||5||4||0||1||+8||12|
|West Ham United||5||3||1||1||+3||10|