United produced a superb attacking display, taking the lead when Nani's cross was turned into his own net by goalkeeper Manuel Almunia after 33 minutes before Wayne Rooney started and finished a stunning counter-attack before half-time.
Park Ji-sung got the third seven minutes after the interval and Arsenal had only the minor consolation of Thomas Vermaelen's deflected volley 10 minutes from time.
"We delivered a completely off-the-mark performance and that's why we were well beaten," Arsenal manager Arsene Wenger said.
"We gave them too much room, we were naive and that's why we have to stick together and produce a much better performance next Sunday when we go to Chelsea."
Arsenal's Andrei Arshavin escaped three times down the left but finished poorly on each occasion while Nani looked highly dangerous down the United right.
It was the 100th Premier League goal of the 24-year-old England striker's career and came just over seven years after he opened his account for Everton against Arsenal when he was 16.
United's third was another long-range break and hesitant defending allowed Park to travel from halfway before calmly slotting his first goal of the season.
Vermaelen's goal led to a brief flurry but United held out quite comfortably and Arsene Wenger's side must bounce back immediately at Chelsea.
"We need to deliver a special performance at Stamford Bridge next Sunday before we can even start thinking about winning the game," Wenger said.
"Arsenal are not out of it, I hope that Arsenal go to Stamford Bridge and batter them," he told Sky Sports.
Ferguson had special praise for the "unbelievable Rooney."
"He was the key player for us and they could just could not handle him. He was a really great player today," he said.
In Sunday's other game, Emmanuel Adebayor marked his return from Togo's traumatic time at the African Nations Cup with the opening goal in Manchester City's 2-0 win over bottom club
