Goals from Mesut Ozil and Alexandre Lacazette proved pivotal as Everton continued their worst start to a season in nine years, with this latest reverse adding to the mounting pressure on Everton manager Ronald Koeman.
German international Ozil struck with a superb header in the 53rd minute at Goodison Park, slipping between two defenders to meet a magnificent left-wing cross from team mate Alexis Sanchez and put Arsenal ahead.
Nacho Monreal had cancelled out Rooney’s opener and hopes of a home comeback were damaged when Everton were reduced to 10 men in the 69th minute after midfielder Idrissa Gueye caught Granit Xhaka and was shown a second yellow card.
Lacazette killed off any hope of that recovery in the 74th minute, after neat passing between Sanchez and Ozil allowed the Frenchman to convert clinically from 15 yards.
The rout continued in the last minute of normal time as substitute Jack Wilshere produced a defence-splitting pass which found Aaron Ramsey who finished unerringly to make it 4-1.
But in a bizarre conclusion, there were two goals in stoppage time, first from Everton substitute Oumar Niasse who charged down a Petr Cech clearance to force the ball into the net.
Arsenal were still not finished and Sanchez became their fifth different scorer from the last attack as he was allowed to carry the ball across the face of the area and score with an excellent angled shot.
Rooney’s goal had come completely against the run of play in the 12th minute but the technique employed by the veteran forward — who turns 32 on Tuesday — was no less impressive for that fact.
Gueye won the ball from Xhaka some 30 yards out and slipped the ball to Rooney, who leant back and guided a perfect finish into the top left-hand corner of the net.
It was the same end and the same top corner as the goal which announced Rooney’s spectacular arrival in the Premier League against the same opponents, 15 years and three days earlier.
But while the Rooney goal that day had won three points for Everton, a repeat of that outcome looked doubtful from early in Sunday’s proceedings.
Aaron Ramsey was denied by goalkeeper Jordan Pickford after just three minutes and a Ramsey cross soon found Lacazette, who showed breathtaking skill to turn his defender and force Pickford into another fine save.
Even after going behind, Arsenal were soon back in the ascendancy with Pickford failing to gather a fiercely-struck Sanchez free-kick but making up for that error by blocking Ramsey’s follow-up attempt from the rebound.
But there was no similar reprieve in the 40th minute when Pickford dived to keep out a drive from Xhaka, which took a deflection off Gyfli Sigurdsson.
The Everton keeper could only push the ball as far as the sprinting Monreal who struck a sweet finish past Pickford for the equaliser.
Everton started the second half brightly but, after Nikola Vlasic ended a promising attack by having a shot blocked, instead of playing in Rooney, Arsenal broke directly upfield for Ozil’s goal.
Lacazette’s goal killed off the contest and, even before the late flurry, there should have been more for the visitors as Sanchez missed with a diving header and Xhaka struck the crossbar with a 20-yard shot. -AFP