Arsenal sent West Brom down with a 3-1 win at the Emirates Stadium as Sam Allardyce suffered relegation from the Premier League for the first time in his career.
The Gunners, 10th in the Premier League table ahead of kick-off and playing for little more than pride after their Europa League exit on Thursday, took the lead when the excellent Bukayo Saka, playing at left-back, crossed for Emile Smith Rowe to volley home (29).
Arsenal doubled their advantage soon afterwards when Nicolas Pepe cut inside from the right flank and curled a stunning effort beyond the outstretched Sam Johnstone (35), but they had some nervy moments after that.
West Brom pulled a goal back in superb style when Matheus Pereira broke forward from inside his own half and, with Arsenal defenders backing off him, fired a diagonal shot into the corner (67).
- How the teams lined up at the Emirates Stadium | Match stats
- Premier League table | Premier League top scorers
The hosts struggled to regain control, despite Mikel Arteta sending on Kieran Tierney, Alexandre Lacazette and Thomas Partey, but Willian eventually made the result safe when he found the top corner with a brilliant free-kick (90) to notch his first Arsenal goal.
Arsenal's first home win in two months was not entirely convincing but it did at least provide some relief after a dismal week. West Brom, meanwhile, return to the Championship after a single season in the top flight.
Arsenal: Leno (6), Chambers (6), Holding (6), Gabriel (6), Saka (9), Elneny (6), Ceballos (6), Smith Rowe (7), Pepe (8), Willian (7), Martinelli (6)
Subs: Lacazette (6), Tierney (7), Partey (6)
West Brom: Johnstone (6), Furlong (6), Bartley (6), Ajayi (6), Townsend (6), Yokuslu (6), Gallagher (6), Phillips (7), Pereira (8), Robinson (7), Diagne (6)
Subs: Robson-Kanu (6), Diangana (6)
Man of the match: Bukayo Saka
How Arsenal sent Big Sam down
Arteta, under pressure after a poor season, had called on his players to show character and desire in the wake of their Europa League exit, but once again they looked flat in the opening stages of the match.
West Brom's direct approach caused them problems, with Kyle Bartley and Semi Ajayi firing long passes over their defence at every opportunity and Pereira twice going close from outside the box, curling one spectacular effort a few inches wide.
Callum Robinson threatened too, sending a looping shot against the crossbar after latching onto a diagonal ball in behind, and while the assistant belatedly raised his flag for offside on that occasion, it served as another warning for the hosts.
- Mikel Arteta made six changes from Arsenal's goalless draw against Villarreal with Pierre-Emerick Aubameyang and Thomas Partey among those dropping to the bench.
- Sam Allardyce brought Callum Robinson and Matt Phillips into the West Brom side. Arsenal loanee Ainsley Maitland-Niles was unable to feature against his parent club.
Arsenal gradually began to wake up, but their build-up play was laboured, with Saka the only player willing to inject speed and urgency into proceedings.
His overlapping runs allowed him to get into dangerous positions repeatedly and while his team-mates were unable to capitalise at first, it was not long until the breakthrough arrived.
Willian played the youngster in behind and Smith Rowe met his fellow academy graduate's cut-back with an impeccably timed run to convert the opening goal.
Arsenal's second came from a rare attack down the opposite flank as Pepe collected Calum Chambers' pass, cut inside West Brom left-back Conor Townsend and picked out the top corner.
Arsenal had chances to further extend their lead before half-time, with Saka once again the source of the danger.
First, his cross was headed over by Gabriel Magalhaes. Then, in first-half stoppage time, his low, diagonal effort was repelled by Johnstone.
Allardyce sent his players out early from the interval but the second half started in the same way the first had ended, with Arsenal threatening to add to their advantage.
Pepe stung the palms of Johnstone with another diagonal effort after West Brom had lost possession in their own half, while Saka continued to find space on the left, with one cut-back narrowly missing both Gabriel Martinelli and Smith Rowe in the six-yard box.
West Brom looked dead and buried at that point but, out of nothing, they pulled a goal back, with the dangerous Pereira capitalising on woeful Arsenal defending as he ran unopposed from the middle of his own half to the edge of the Gunners' box and fired a clinical effort into the bottom corner.
Arsenal were rocked by the goal and struggled to regain control as West Brom sensed an opportunity to draw level. It looked like they might in the 73rd minute when Darnell Furlong met a Matt Phillips cross - only to head wastefully wide.
It was a fortunate escape for Arsenal and it was the closest West Brom came to prolonging their Premier League survival.
The Gunners then made the result safe when the much-maligned Willian provided a reminder of his quality, curling home a free-kick from 25 yards out and sealing what is only Arsenal's seventh home win of a difficult Premier League campaign.
Man of the match - Bukayo Saka
With Tierney on the bench and Granit Xhaka injured, Saka started at left-back for only the second time all season. His performance was one to savour - although some Arsenal fans will see it as proof that he should have been deployed there earlier.
The 19-year-old, like Smith Rowe, has provided a ray of light in a dismal season and while he has shone in more advanced roles over the course of the campaign, this was a reminder of just how dangerous he can be from the left-back position.
West Brom could not handle his speed and directness and while the statistics show he only created two chances, there were many more occasions when he got in behind and created danger for his side.
Arsenal's squad is in need of work but in Saka they have a player to build around.
What the managers said...
Mikel Arteta: "We needed that win. It has been a while since we won at home. We scored three fantastic goals and we had some great spells in the game.
"They scored out of nothing and then they throw everything at you. They know the situation they are in and we struggled to play that kind of game. When we conceded the goal we did look nervy.
"Europe is a completely different game, different context. There were things we could have done much better.
"We will try to win every match now and see where we finish. The only thing we can do is win our games."
Sam Allardyce: "It's not sunk in yet, but I'm sure I'll wake up tomorrow and realise the situation. I'm bitterly disappointed we're not still in the fight.
"I'm not saying we would have avoided relegation but we should have been closer, we should have taken it down to the last three games, based on how we performed. The creating of chances has been there but the converting has not.
"We had [enough] time to pull it round. Our real problem was not beating the bottom-six sides when we came up against them. The results against Chelsea, Manchester United and Manchester City should have been bonus points."
Opta stats - West Brom's sinking feeling
- West Brom have suffered their fifth relegation from the Premier League, the joint-most by a team alongside Norwich City, whilst Sam Allardyce has been relegated from the top-flight for the very first time in his managerial career.
- Arsenal have recorded back-to-back Premier League victories for just the second time in 2021, having previously done so back in January.
- Of the five relegations that West Brom have suffered from the Premier League, only in 2002-03 (4) have the Baggies had their relegation confirmed with more games remaining than this season (3).
- Arsenal are unbeaten in their last 30 Premier League home games against promoted (W25 D5), with their last such defeat coming back in November 2010 against Newcastle.
- West Brom boss Sam Allardyce has failed to pick up a single point in his 10 Premier League trips to the Emirates Stadium, with only Harry Redknapp at Old Trafford (15 visits) managing more matches at a single venue without managing to earn at least one point in the competition.
- Bukayo Saka's assist for Emile Smith Rowe's opening goal was his 19th in the colour of Arsenal since making his debut in November 2018, more than any other player at the club.
- Emile Smith Rowe is the fourth player aged 21 or under to score for Arsenal in the Premier League this season (along with Saka, Martinelli and Nketiah) - no team have had more different U21 scorers in the competition this term.
- Matheus Pereira is the first West Bromwich Albion player to reach 10 goals in a Premier League campaign since Saido Berahino managed 14 goals back in 2014-15.
Live Premier League
Live Renault Super Sunday
Arsenal are back in action on Wednesday when they travel across London to face Chelsea, live on Sky Sports; kick off 8.15pm.
Meanwhile, West Brom face Liverpool next Sunday, also live on Sky Sports; kick off 4.30pm.