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.
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.
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.
"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."
