Thierry Henry and Robert Pires struck to clinch opening day victory for ten-man Arsenal after Sol Campbell was sent off for a professional foul.
Tomasz Radzinski replied six minutes from time for Everton who had failed to capitalise after Campbell's 25th-minute dismissal.
Referee Mark Halsey red-carded Campbell, the last defender, for a professional foul on Thomas Gravesen. It was Campbell's third sending-off as an Arsenal player.
Halsey had also sent off Campbell against Manchester United near the end of last season for elbowing Ole Gunnar Solskjaer, a crucial blow to Arsenal's title chances.
The Gunners also had Francis Jeffers sent off last weekend in the Community Shield.
Everton finished with ten men too, after substitute Li Tie was dismissed in the 87th minute for two yellow cards, both for fouls on Ray Parlour.
Campbell's early exit galvanised Arsenal who had made a sluggish start against hard-working opponents. Henry shot the Gunners ahead from a 35th-minute penalty after Alan Stubbs handled his attempted shot.
They pummelled Everton for most of the second half. Patrick Vieira headed wide from a corner before Pires netted their second.
Keeper Richard Wright made brilliant saves from Henry and Vieira but he was helpless as Pires swept in from six yards.
Wright then kept his side in contention with a point blank parry from Vieira.
Everton lacked penetration without the suspended Duncan Ferguson and injured Kevin Campbell.
Manager David Moyes was forced to gamble on Wayne Rooney as a second half substitute despite his recent ligament trouble.
Rooney was booked for a foul on Kolo Toure, but did supply the pass for Radzinski to shoot home from 18 yards. Joseph Yobo was off target with a late header as Everton's fight back came to nothing.