Giroud, who had not scored in all competitions since November 23, got the faintest of touches to glance a Theo Walcott free kick into the net midway through the second half.
Romelu Lukaku, who had not scored for Everton in five games, scored the winner for Roberto Martinez's side three minutes after Gaston Ramirez cancelled out Seamus Coleman's early opener.
Arsenal, with 42 points, are one point clear of Manchester City after 19 games. Everton, in fourth on 37, leapfrog rivals Liverpool, who play Chelsea later on Sunday.
Tottenham Hotspur host Stoke City in Sunday's other match.
(Reporting by Toby Davis; editing by Justin Palmer)
