Wigan is going down to the League Championship, and Arsenal is in position to reach the Champions League for the 16th straight season.
Wigan became the first team to win the FA Cup and get relegated in the same season, losing 4-1 at Arsenal on Tuesday night.
"We've had an incredible eight years in the Premier League, and we have to take the good things from last few years, and there are many," Wigan manager Roberto Martinez said. "We'll bounce back, as we always do at Wigan. We're on a fantastic financial footing, we have huge assets and a philosophy for the long-term."
Lukas Podolski put Arsenal ahead in the 11th minute. Coming off Saturday's FA win over Manchester City, Wigan tied the score on Shaun Maloney's goal from a free kick in the 45th.
The Gunners broke open the game with three goals in an eight-minute span, by Theo Walcott in the 63rd, Lukas Podolski in the 68th and Aaron Ramsey in the 71st.
"The FA Cup gave us a bit of hope to finish the season in the league on a real high. The youngsters came in and gave us a different sense of confidence," Martinez said. "It was great to win the FA Cup _ that will live forever for the fans. Today is really disappointing, but it is something we can rectify. It's a difficult time but it's time to look back, get stronger and prepare for the future."
Walcott scored the go-ahead goal when he received a low cross from Santi Cazorla and nudged the ball over goalkeeper Joel Robles, who slid studs-first rather than dive and use his arms.
"It is sad that they go downm because they are a good team, they play good football and are an intelligent team with good players," Arsenal manager Arsene Wenger said. "If they stay together, they will certainly come up again.
Arsenal (20-7-10) moved into fourth place with 70 points, one above Tottenham (20-8-9) for England's final Champions League berth next season.
Arsenal closes at Newcastle on Sunday, when Tottenham hosts Sunderland. Chelsea (21-7-9), third with 72 points, is virtually assured of a Champions League berth because of a far superior goal difference to Tottenham's (plus-35 to plus-19).
"It is all open, but it depends on our result," Wenger said. "Even third place is not out of sight if we win the game."
Wigan (9-19-9), which has allowed a league-high 71 goals, joined Reading (6-21-10) and Queens Park Rangers (4-20-13) as the teams going down to the second-tier League Championship next season.
Cardiff and Hull have earned promotion to the Premier League and will be joined by the winner of the Crystal Palace-Watford playoff final on May 27.
While Arsenal has failed to win any trophies since 2005, fans remained to cheer Wenger and the Gunners after their final home match. From jeers in October to cheers in May _ the fans in the rain sang "There's only one Arsene Wenger!"
Next week he'll become the longest-serving current Premier League manager when Manchester United's Alex Ferguson retires.
In the night's other Premier League match, Manchester City won 2-0 at Reading, a day after the 2012 champions fired manager Roberto Mancini. Sergio Aguero scored in the 40th minute and Edin Dzeko in the 88th as City (23-5-9) clinched second place.
Please Wait…