A high-tempo, top quality game was decided by two Rashford goals on the break after Bukayo Saka had cancelled out United debutant Antony’s opener.
Arsenal remained top of the table on 15 points thanks to their opening five wins and while they will be disappointed to have ended that run, this was far from the kind of meek loss against Big Six opponents they have produced in the recent past.
United look to have found their belief again after starting the campaign with dreadful defeats by Brighton and Brentford and Dutch coach Erik ten Hag’s approach is bringing results.
Antony was handed a place on the right flank with Rashford central and Jadon Sancho on the left but Cristiano Ronaldo started on the bench alongside Brazilian Casemiro.
United dominated the opening exchanges, camping in Arsenal’s half and there was an early chance for Christian Eriksen but the Dane’s volley flashed wide.
Arsenal looked slick on the ball, though, and Gabriel Martinelli looked to have given them a 12th-minute lead after finishing off a swift break.
But referee Paul Tierney was sent to the monitor and disallowed the goal after ruling that Eriksen had been fouled by Martin Odegaard before the counter-attack was launched.
Martinelli forced two saves from United keeper David De Gea as the visitors began to dominate but it was the home side who drew first blood, 10 minutes before the interval.
Brazilian Antony, signed from Ajax last week, was found on the right by Rashford and coolly drifted a left-foot shot into the far bottom corner.
Arsenal deservedly drew level, on the hour, when the outstanding Odegaard threaded a ball towards Gabriel Jesus in the box and after a challenge by Raphael Varane the ball fell to Saka who slotted home.
United might have panicked or faded away last season but six minutes later they restored their lead when Bruno Fernandes found Rashford with a superb through ball and the England striker confidently beat the advancing Aaron Ramsdale.
It was another swift counter that led to United’s third with the excellent Erkisen breaking clear and slipping the ball across to Rashford for a simple finish.
A four-game winning run, including victories over Liverpool and Arsenal, has totally changed the mood at Old Trafford and Ten Hag was rightly pleased with his players’ resilience.
“The spirit from this team, they can deal with setbacks so we did, it is really great and shows your mentality – we have really improved on that,” he said.
“We are happy and satisfied with the win, also the performance against a really good team – they played really well,” he said.
United climbed to fifth in the standings, three points behind Arsenal.