Andre Marriner dismissed Arsenal defender Kieran Gibbs instead of teammate Alex Oxlade-Chamberlain, whose diving save with his hand blocked the ball on the goal-line.
The 15th-minute sending off was hardly a turning point in the London derby, however, as Arsenal had already conceded twice inside seven minutes of Wenger's landmark match. And Arsenal crumbled further against the leaders after Eden Hazard converted the penalty kick, dropping to fourth in the standings as their title rivals all won.
"It's one of the worst days (in my career)," said Wenger, who uncharacteristically did not attend the post-match news conference. "It's over after 20 minutes and it's a long game after that."
Manchester City climbed above Arsenal into third place with a 5-0 victory over Fulham, while second-place Liverpool won 6-3 at Cardiff. It leaves Chelsea four points ahead having played one more than Liverpool and three more than City, which is six adrift.
Far from the title race is Manchester United, which remains seventh despite Rooney scoring twice — the first a volley from the halfway line — in a 2-0 victory at West Ham.
The bottom three remains unchanged with Fulham in last place behind Cardiff and Sunderland, which lost 2-0 at Norwich after conceding goals from Robert Snodgrass and Alexander Tettey. Hull surged eight points clear of danger after Shane Long and Nikica Jelavic clinched a 2-0 victory over West Bromwich Albion.
Everton moved ahead of Tottenham into fifth after Ross Barkley's header secured a 3-2 victory over Swansea, and Newcastle climbed to eighth by defeating Crystal Palace 1-0 after Papiss Cisse scored in stoppage time.
Chelsea raced in front at Stamford Bridge, with Andre Schuerrle setting up Samuel Eto'o to curl in the opener in the fifth minute and then scoring himself two minutes later to complete another rapid break.
After Hazard's penalty following the red-card confusion, Fernando Torres squared for Oscar to scoop in Chelsea's fourth just before halftime. Oscar netted again in the 66th after a curling shot slipped through Wojciech Szczesny's hands, and the goalkeeper allowed Salah's shot to roll under him four minutes later to complete Jose Mourinho's biggest win as Chelsea manager.
The margin of this defeat matched the previous low-point of Wenger's 18-year reign — an 8-2 loss at Manchester United. It was also Arsenal's third big away loss against its direct title rivals this season, following a 6-3 defeat at Manchester City and 5-1 drubbing at Liverpool.
City also hit five on Saturday, with Yaya Toure contributing a hat trick.
The first two came from penalties — in the 26th and 54th, both times after fouls by Fernando Amorebieta, who was sent off after the second — and curled in the third in the 66th. Fernandinho and Martin Demichelis added late goals.
Rooney's first double in almost four months taking him to third place among United's all-time scorers.
With David Beckham watching in the stands, Rooney replicated one of the retired star's most memorable goals for the club in August 1996.
Rooney spotted Adrian off his line in the seventh minute and the goalkeeper was helpless to get back in time.
"It's just instinct, I've turned and had a quick look and seen the goalkeeper off his line," Rooney said. "It's one of those I've tried many times and thankfully today it's gone in."
The England striker slotted in his 212th United goal in the 33rd after Mark Noble failed to fully clear Ashley Young's low cross.
The most goals of the day came in south Wales as Liverpool twice came from behind.
Luis Suarez cancelled out Jordon Mutch's opener for Cardiff, the first of three goals for the Uruguay striker. Although Frazier Campbell restored Cardiff's lead, Martin Skrtel levelled and put the visitors in front for the first time early in the second half.
Suarez added two more, and Daniel Sturridge also found the net, while Mutch headed in his second for Cardiff.