The wily Wenger could face disciplinary action after blatantly shoving Chelsea's manager in the chest midway through the first half after a heated exchange of views.
It was Mourinho, as is usually the case, who had the last laugh though with goals from Eden Hazard and Diego Costa clinching the honours to stretch Chelsea's lead at the top to five points ahead of the international break.
Mourinho is yet to taste defeat when up against Wenger, winning seven and drawing five of their clashes, and while he has often appeared to go out of his way to irritate the Arsenal boss, he appeared the innocent party on Sunday.
"There are two technical areas, one for me and one for him and he was coming to my technical area and not coming for the right reasons," Mourinho told reporters. "I didn't like that."
Wenger tried to play down the incident afterwards, saying he had merely been trying to get from "A to B" when Mourinho got in the way, although he will await any action from the FA.
Chelsea were not at their fluent best but for all Arsenal's possession they rarely looked like replying once Hazard had earned and converted a 27th minute spot kick.
The hosts appeared content to sit back in the second half until former Arsenal skipper Cesc Fabregas, up against the club he made more than 300 appearances for, for the first time since returning to the Premier League from Barcelona, sent Costa clear with 12 minutes remaining to wrap up the points.
Spain striker Costa had been quiet throughout but took his tally to nine league goals in seven matches for the Blues.
"When it was 1-0 I felt we had the game in our pocket," Mourinho said. "I was very pleaed because we played against a good Arsenal and they gave us a difficult game, but we dealt with them without problems."
The only worry for Chelsea was a first-half head injury to keeper Thibaut Courtois who soldiered on for a while before being replaced by Petr Cech.
After a 15-minute delay caused by an incident with a flare outside the stadium, the opening half proved a feisty affair.
Arsenal began in confident fashion with Alexis Sanchez having the first shot in anger and the Chilean remained in the thick of the action when, minutes later, he stretched to reach a Jack Wilshere through ball clattered into Courtois.
Sanchez was then on the receiving end of a hefty challenge from Gary Cahill that had Wenger so incensed he stormed into Mourinho's technical area.
When Mourinho confronted the Frenchman, Wenger offered a two-handed shove into the chest of the Portuguese who last season described his rival as a "specialist in failure".
The incident raised the decibel level in the stadium and sparked the hosts into life.
Shortly after a still groggy Courtois was helped off, Chelsea took the lead.
Hazard's swerving run was ended abruptly by Laurent Koscielny for a penalty that the Belgian slotted home.
Arsenal playmaker Mesut Ozil flitted in and out of the game and ironic home cheers greeted one tackle on the German by Fabregas who displayed calm authority throughout a tetchy game.
Hazard tormented Arsenal's young left back Calum Chambers and one cross from the fleet-footed Belgian was almost sliced into his own goal by Mathieu Flamini.
Any hope Arsenal had of salvaging a point were dashed when Fabregas, perhaps lucky not to concede a penalty earlier when he blocked Wilshere's shot with his arm, lofted a ball forward for Costa to race clear and lob Wojciech Szczesny.
(Reporting by Martyn Herman; editing by Justin Palmer)
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