The victory is Everton’s third in a row in the league, while Arsenal’s poor away form has continued.
The Gunners remain fourth in the Premier League table, but are vulnerable to fifth-placed Chelsea and sixth-placed Manchester United as the battle for the Champions League positions intensifies.
Arsenal had a good chance to register in the first two minutes when Alexandre Lacazette broke into a dangerous position before feeding Mesut Ozil, but eventually Everton managed to clear their lines after a period of panic.
It was the home side that made the breakthrough in the 10th minute, though, and it came from a player who was not originally due to start.
Indeed, Jagielka was a late introduction after Michael Keane was taken ill ahead of kickoff and the experienced centre-back converted from close range after Arsenal had failed to deal with a corner kick.
Andre Gomes tried his luck for Everton in the 16th minute as the home side looked to double their advantage, but the on-loan midfielder’s effort was always moving wide of the post.
The Gunners have still not kept a single away clean sheet in the Premier League this season and looked capable of shipping more goals at Goodison as the team in blue continued to throw players forward.
Idrissa Gueye was next to try his luck for Marco Silva’s side in the 25th minute, but his strike was always moving wide of the Arsenal post.
Gylfi Sigurdsson then struck into the arms of Bernd Leno in the 37th minute after the Iceland international found all sorts of space in the gap between Arsenal’s midfield and three centre-backs.
Gomes was running the show for the Toffees in the middle of the park, with Arsenal struggling to get hold of the ball and the two teams headed down the tunnel at the interval with Jagielka’s goal the difference.
Pierre-Emerick Aubameyang and Aaron Ramsey both came off the Arsenal bench at the break and the latter had a wonderful chance to level the scores early in the second period. Indeed, the ball fell for the Wales international in a dangerous position, but he somehow missed the target.