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 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.
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.
Arsenal (20-7-10) improved to 70 points, one above fifth-place 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).
Wigan (9-19-9), which has allowed a league-high 71 goals, joined Reading (6-20-10) 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.