The Red Devils came back from a Lisandro Martinez own goal in the first half to come from behind to win 3-2.
Bryan Mbeumo took advantage of a Martin Zubimendi error to equalize before Patrick Dorgu put the visitors ahead with a stunning goal.
Mikel Merino leveled matters in the 84th minute to give the Gunners hope of a win, but Matheus Cunha broke their hearts moments later with a fantastic finish of his own.
Carrick has now guided United to victory over Manchester City and Arsenal in his first two games as interim head coach, moving them up to fourth in the Premier League. While his side dominated City last weekend, he felt they had to roll with the punches this time.
Michael Carrick ‘extremely proud’ as Man Utd shock Arsenal
“Yes, very proud,” he told Sky Sports. “I think it was different from last week – two very different games. It was always going to be different today. They put a lot of pressure on us in different ways.”
“We probably didn’t have as much of a real, regular threat in the game as we did last week, but I thought there were periods where we looked really dangerous, to come here and score three goals in the way we did. One down, coming back, then the setback and still going – it was a huge moment for us.”
“The boys had to put in a lot of effort today. It probably wasn’t as easy as last week. Last week the time, the flow of the match and the momentum were with us almost the entire time, while today we had to dig deep. It was a huge effort and I’m really proud of them.”
Read – Premier League Team of the Week: Fernandes, Estevao, Dorgu
See also – Eight moments that defined the classic rivalry between Arsenal and Man Utd
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