Wenger was sent from the dug-out for kicking away a water bottle after Robin van Persie's stoppage-time strike was disallowed for offside, with United having come from behind to lead with a Wayne Rooney penalty and an Abou Diaby own goal.
It was a frustrating game for Wenger, who watched the final stages perched on a ledge being baited by joyous United fans who must have doubted their team's chances after Arsenal had made much the better start.
Andrei Arshavin's fierce drive had given the Gunners the lead and only an instinctive save from Ben Foster prevented Van Persie doubling their advantage shortly after the break.
United levelled when Rooney was brought down in the area by Arsenal keeper Manuel Almunia as he collected a Ryan Giggs pass and the England striker converted the penalty for his fourth goal of the season.
Five minutes later Giggs crossed and an off-balance Diaby headed past Almunia to condemn the Gunners to defeat after they had won their first two league games by 6-1 and 4-1 margins.
United managed just one victory in their clashes against top four teams last season and Rooney said it was an important win, especially as the champions have already lost this season at newly-promoted Burnley.
"Our record last season against the big teams wasn't great and Arsenal have started the season well while we've lost already, so we needed to win today," Rooney told Sky Sports.
United were poor in the first half, with precious little service to the hard-working Rooney.
Arsenal might have had a penalty when Arshavin was scythed down by Darren Fletcher.
They did not have to wait long for their opener, however, as Russian Arshavin found himself in space 25 metres out, and smashed a rising shot past the despairing dive of Foster.
Arsenal sliced United open again early in the second half when Arshavin played the ball across the area to Van Persie who saw his close-range flick saved by the boot of Foster on the line. It was to prove a turning point.
"We performed really well in the second half," United manager Alex Ferguson said. "We had a bit of luck with the own goal but it was a clear penalty."
Wenger praised his team's performance and believed his team had been unlucky.
"It was frustrating to go home without any points after playing like that," Wenger told Sky Sports, confirming that he was sent from the dugout for kicking a water bottle.
Thank you for reading 5 articles this month* Join now for unlimited access
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Join now for unlimited access
Try first month for just £1 / $1 / €1