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Stunning goals from Nicolas Pepe and Willian earned Arsenal a 3-1 home win over West Bromwich Albion that confirmed the Baggies' relegation.
West Brom had to at least draw but realistically needed a win to keep their hopes of safety alive, due to their goal difference.
Matheus Pereira twice went close for them early on, but Arsenal took the lead just before the half-hour mark with Emile Smith Rowe's fine volley from Bukayo Saka's cross.
Pepe cut in and curled a spectacular shot beyond Sam Johnstone to make it 2-0 on 35 minutes.
Pereira pulled a goal back after 67 minutes with a low finish following a solo run from his own half.
Darnell Furlong headed wide as West Brom pressed for an equaliser, but Willian wrapped up the win for Arsenal with a sublime 90th-minute free-kick.
Defeat leaves West Brom 19th on 26 points, 10 points behind 17th-placed Burnley with three matches left.
Arsenal, in ninth, move up to 52 points.
See: Arsenal report | West Brom report
Next fixtures
Arsenal: 12 May v Chelsea (A)
West Brom: 16 May v Liverpool (H)
Match officials
Referee: Peter Bankes. Assistants: Neil Davies, James Mainwaring. Fourth official: David Coote. VAR: Mike Dean. Assistant VAR: Dan Robathan.
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