Newcastle's Joelinton shot wide while Arsenal duo Pierre-Emerick Aubameyang and Eddie Nketiah were denied by Martin Dubravka in a goalless first half.
Nketiah hit the crossbar early in the second half before Aubameyang headed in from Nicolas Pepe's cross to put Arsenal in front after 54 minutes.
The Gunners doubled their advantage within three minutes, Bukayo Saka winning the ball from Valentino Lazaro and crossing for Pepe to steer past Dubravka.
Allan Saint-Maximin hit the post before Mesut Ozil's close-range effort and substitute Alexandre Lacazette's strike wrapped up the win during stoppage time.
A first win in five matches moves Arsenal up to 10th place with 34 points, three clear of 13th-placed Newcastle.
Arsenal: 23 Feb v Everton (H)
Newcastle: 22 Feb v Crystal Palace (A)