The France international produced a brilliant performance in the middle of the park in the opening 74 minutes at the Emirates Stadium.
Pogba played a key role in helping Manchester United stand-in captain Antonio Valencia to break the deadlock in the fourth minute in north London.
Anthony Martial teed up England international Jesse Lingard to extend the visitors’ lead in the 11th minute to put Manchester United in a commanding position.
Arsenal threatened to mount a comeback when Aaron Ramsey combined with Alexandre Lacazwette before the Gunners record signing finished past David De Gea.
Pogba produced his best moment of the match when showed supreme strength to hold off Laurent Koscielny before he squared a pass to Lingard at the far post to make it 3-1.
However, the 25-year-old’s evening ended on a sour note when Pogba received a straight red card for a nasty challenge on Hector Bellerin.
While the tackle appeared to be more mistimed than malicious, the France star will miss next weekend’s Manchester derby against the Premier League leaders due to suspension.
Asked during his interview with BT Sport about Pogba’s red card and subsequent suspension, Mourinho replied:
“I don’t know. I leave for you that one. I leave for you the Lukaku situation with Koscielny, I leave for you the Arsenal players on the grass.
“The grass is absolutely beautiful – I think there is a desire to go onto the grass.”
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