Chelsea consolidated its lead in the Premier League by beating London rival Arsenal 2-0 on Sunday in a feisty encounter that may be best remembered for Wenger losing his normal cool and giving Mourinho a shove in the chest on the sideline.
Former Arsenal captain Cesc Fabregas set up the second goal for Diego Costa in the 78th minute to make sure Chelsea remained five points clear of defending champion Manchester City atop the standings. Arsenal is now nine points behind in eighth place, having failed to avenge a 6-0 drubbing at Stamford Bridge last season.
Both Manchester United and Tottenham climbed above Arsenal with wins.
United beat Everton 2-1 to climb to fourth after goalkeeper David de Gea saved a penalty and made two crucial stops to deny the visitors a late equalizer at Old Trafford. Tottenham is sixth after Christian Eriksen scored in the 40th minute to secure a 1-0 win over Southampton.
Also Sunday, Queens Park Rangers dropped to the bottom of the standings after losing 2-0 to West Ham.
The Chelsea-Arsenal game was always going to be emotional given Wenger's humiliation at Stamford Bridge in his 1,000th game in charge last season along with Fabregas facing his former team. It even turned physical in the dugout after a hard foul on Alexis Sanchez, with an angry Wenger squaring up against Mourinho and then giving the Portuguese manager a shove in the chest before being separated by the fourth official.
Both coaches downplayed the incident after the game, after Mourinho's side once again had the better of Wenger's on the pitch.
Wenger described the push as just "a little one" and said "what is to regret after that?"
Mourinho said everyone should "forget" the incident.
"To be fair, I do so many wrong things in football," Mourinho said. "But not this time, because this time I was just in my technical area and it was not my problem. Game over. Story over."
Arsenal's title push may not be quite over yet, but a nine-point gap is looking rather large even this early in the season given Chelsea's strong form.
Eden Hazard weaved inbetween defenders in the 27th minute before being tripped by Laurent Koscielny in the area, and then converted the ensuing penalty himself to put Chelsea ahead. With Arsenal pushing for an equalizer, Fabregas picked the defence apart in the 78th with a pinpoint long ball up to Costa, who lobbed the ball into the net with one touch.
In Manchester, Radamel Falcao scored his first goal for United as the Red Devils won consecutive Premier League games for the first time under manager Louis Van Gaal.
Angel Di Maria opened the scoring for the hosts before De Gea saved a penalty from Leighton Baines just before halftime. Baines then picked out Steven Naismith, who put the teams level in the 55th, but Falcao sealed his team's win seven minutes later by slotting home past Tim Howard after di Maria's shot landed in the Colombian's path.
De Gea made a stunning save in stoppage time to tip over the bar Bryan Oviedo's left-foot shot from 20 metres.
"What was my most important save? Maybe the penalty," De Gea said. "Every save is important but the team played very well. I think the younger players in the team will learn from these types of games. The team and the manager need to look forward."
Mauricio Pochettino got the better of his Southampton successor Ronald Koeman as Tottenham ended its four-match wait for a Premier League win.
Eriksen scored with a 20-yard strike in the 40th minute to deny Koeman's side a seventh straight win in all competitions.
Pochettino took on his former club for the first time since ending a successful 18-month stint at St Mary's to lead Spurs.
At Upton Park, Nedum Onuoha's own-goal gave the Hammers an early lead against QPR before Diafra Sakho headed home a second shortly before the hour mark.