Goals for Alexis Sanchez and Mesut Ozil saw the Gunners, lining up with a three-man defence, record just their second win in six Premier League games as they concluded the top-flight Easter action.
On Sunday, Chelsea lost 2-0 to Manchester United at Old Trafford to ensure Arsenal's north London rivals Tottenham ended the weekend just four points behind the league leaders in the title race.
Spurs beat Bournemouth 4-0 on Saturday to cut the Blues' lead at the top of the table, with Mousa Dembele, Heung-min Son, Harry Kane and Vincent Janssen were all on target.
EPL Table | Premier League standings after Gameweek 33
The momentum is with Tottenham, who have stepped up by winning seven Premier League games in a row for the first time in their history, and Chelsea's defeat at Old Trafford - courtesy of goals from Marcus Rashford and Ander Herrera - opens up a chance for Spurs to further capitalise during the run-in.
Earlier on Sunday, Liverpool earned a hard-fought 1-0 win away at West Brom to further dent Arsenal's top-four hopes. The Gunners have played three games less than their Anfield counterparts.
The rest of Saturday's action saw Crystal Palace fought back from two goals down to secure a creditable 2-2 draw with champions Leicester.
Sam Allardyce's side are seven points clear of the drop zone and - if their form continues - look set to retain their top-flight status.
West Ham squandered a lead deep into injury time at Sunderland, with Fabio Borini's equaliser keeping the Black Cats' slender hopes of survival alive.
Everton climbed to fifth place courtesy of a 3-1 victory over Burnley but the majority of the Toffees' rivals still have crucial games in hand.
Meanwhile, Stoke eased past Hull while Watford cemented their position in the top half of the table with a 1-0 victory over relegation-threatened Swansea.