Substitute Manolo Gabbiadini brought Southampton close to safety as they saw off Swansea 1-0 at the Liberty Stadium, confirming West Brom’s relegation from the Premier League.
The result means Swansea must hope they beat Stoke on Sunday and Huddersfield lose their last two games, while Southampton will be safe barring a defeat against Manchester City and a large goal swing towards Swansea.
Gabbiadini grabbed the winner with 17 minutes remaining after a scramble inside the penalty area, one of few clear-cut opportunities in a nervy encounter.
With so much at stake, the first half was a cagey affair, with half-chances falling to Sam Clucas and Charlie Austin inside the penalty area, but things picked up in the second.
Jordan Ayew forced a wonderful fingertip save from Alex McCarthy having cut inside from the left and unleashed a fine effort from 20 yards which was bound for the top corner.
Saints should have been ahead on the hour mark, but Austin’s header in space eight yards out from Cedric Soares’ cross was straight at Lukasz Fabianski.
But on 72 minutes they did break the deadlock as sub Gabbiadini, who had been on the pitch for just five minutes, drove home from close range after Alfie Mawson had blocked Shane Long’s volley on the goal line.
Gabbiadini’s substitution was a result of luck and a brave move by Mark Hughes, with the Italian striker replacing defender Jan Bednarek, who had concussion but did not want to be taken off.
Shane Long missed a chance to wrap it up late on, hitting into the side-netting when the square pass to the unmarked Gabbiadini seemed the better option, but after a nervy finish, Mark Hughes’ side held on.
Swansea host Stoke on Sunday in their final Premier League game, while Southampton welcome champions Manchester City to St Mary’s.