The only low point was Jagielka getting a second yellow for hauling down Lucas Perez in the dying minutes and their captain now misses next week’s Merseyside derby.
But that could not spoil the night as Goodison roared with delight.
EVERTON (4-2-3-1): Stekelenburg; Coleman, Jagielka, Williams, Baines; Gueye, McCarthy (Funes Mori 90); Valencia (Calvert-Lewin 79), Barkley, Lennon (Mirallas 68); Lukaku. Subs: Robles, Deulofeu, Cleverly, Holgate.
ARSENAL (4-2-3-1): Cech; Bellerin, Gabriel, Koscielny, Monreal; Coquelin (Perez 88), Xhaka; Walcott (Giroud 71), Ozil, Oxlade-Chamberlain (Iwobi 71); Sanchez. Subs: Ospina, Gibbs, Holding, Iwobi, Elneny.
REFEREE: Mark Clattenburg