Michael Essien scored twice to inspire Chelsea to their fourth Premier League win in four matches. The champions strolled to a 3-1 victory at West Ham United, leaving their London rivals rooted to the foot of the table with no points.
Arsenal took full advantage of a red card for Bolton Wanderers defender Gary Cahill with a 4-1 home triumph.
Moussa Dembele's second goal of the game, in the last minute, gave Fulham a 2-1 win over Wolverhampton Wanderers that was soured by a broken leg for England striker Bobby Zamora.
Goalkeeper Matt Gilks was man of the match as Blackpool continued an impressive start to their first top-flight season for 39 years with a 2-0 victory at Newcastle United.
Manchester City struggled again, held 1-1 at home by Blackburn Rovers. Tottenham Hotspur's Luka Modric joined the club's growing injury list despite scoring in a 1-1 draw at West Bromwich Albion.
There was a real buzz around Goodison Park with the news that United and England striker Rooney, at the centre of tabloid allegations over his private life, had been left out.
It looked to be a good decision as the visitors cruised into a 3-1 lead after goals by Darren Fletcher, Nemanja Vidic and Dimitar Berbatov had cancelled out Steven Pienaar's 39th-minute opener for Everton.
However, in a breathless finale, Tim Cahill headed Everton's second in the first minute of added time and Mikel Arteta kept his cool to rifle in the equaliser after spring-heeled Cahill had nodded down another Leighton Baines cross.
QUITE UNREAL
"It's quite unreal but with the chances we missed it was probably a fair result," Cahill told Sky Sports.
United manager Sir Alex Ferguson, who also saw his team concede a last-minute equaliser at Fulham last month, said: "Football can do that to you. From a completely comfortable position we've thrown it away.
"We played some good football at times and Berbatov was absolutely brilliant but that's all wasted."
On Rooney's omission, Ferguson said: "We made a decision simply because he gets terrible abuse here. We don't want to subject him to that."
Soon after United trudged off the pitch in their lunchtime kickoff, Chelsea were already ahead at a West Ham side struggling under new boss and former Stamford Bridge manager Avram Grant.
The champions might have been handed a gentle start to the season fixture-wise but they have taken full advantage by winning all four games, scoring 17 goals and conceding one.
After Essien headed in a second-minute corner, goalkeeper Robert Green and defender Matthew Upson gifted Salomon Kalou a lucky second as the ball rebounded off him and looped into the net.
Essien doubled his tally with another late header - Didier Drogba claiming a hat-trick of assists - while Scot
