Jose Mourinho introduced Marcus Rashford and Jesse Lingard to try to rescue the game, but they failed to bring the visitors to life.
To end United's 25-game unbeaten run with such an impressive performance was special, even if Wenger would not to admit it.
"[Mourinho] He would be foolish to throw it away and bank on the Europa League, which English teams don't exactly have much of a record in". Now, the competition could be his savior. Several of their first-team players did not play in their 3-0 loss to Athletic Bilbao last weekend, in the hope that they can play a rejuvenated side against Manchester United.
Goals from Granit Xhaka and Danny Welbeck finally gave Wenger his first win in 13 attempts against Mourinho in the Premier League. He is a big manager.
"The Arsenal fans, they are happy", Mourinho said.
"I leave Highbury they were crying". Arsenal have plenty of work left ahead them, but a season that has teetered on the brink of disaster could yet end with a Champions League place and a trophy.
With the Europa League final in sight, Manchester United head to northern Spain this week to play Celta Vigo.
Proceedings had long since lost any real tempo, though, and Arsenal comfortably held on to move to within two points of United and six of Manchester City, while the Gunners still have a game in hand on both.
With Mourinho's side lying fifth in the Premier League, the Europa League could represent their best chance of reaching next season's Champions League.
Celta coach Eduardo Berizzo was also full of admiration for Rashford after the Spanish side's first major European semi-final ended in a narrow loss.
And what did Neville make of Arsenal? The striker has now scored in each of his last three appearances against his old club.
"(Arsenal) had a bit of luck with their first goal", Mourinho said. They had the luck of that goal, and we didn't score before them.
"Thursday is the match of the season".
James Milner stepped up to take the spot kick but Fraser Foster dived down low to his right to save his effort and the match finished 0-0. The penalty was awarded for a handball against Jack Stephens.
"In relation to the Premier League, I think it is too late because in the past month of April we played nine matches - seven of them in the Premier League and we had too many problems, we had too many players absent".
If United qualify and finish outside the top four, will a top-four team miss out?