United manager Alex Ferguson called Rooney, who had all four goals against Hull City a week earlier, "unbelievable."
"He was the key player for us," said Ferguson, "and they could just could not handle him. He was a really great player today."
Nani wasn't too bad, either.
On the first goal, the 23-year-old winger lobbed Manuel Almunia from a sharp angle after beating Arsenal players Gael Clichy and Samir Nasir, and all the Gunners keeper could do was palm the ball into his goal.
Nani fed Rooney for the second goal that completed a devastating counterattack that started when Park Ji-Sung won the ball in the United penalty area and fed Rooney outside the United box.
"That was my best game," said Nani. "I played well, scoring and getting an assist. I can feel the confidence of my teammates, the fans and the manager."
Park put the game away with the third goal in the 52nd minute.
Rooney and Nani both had chances to add to United's lead before Belgian Thomas Vermaelen scored a late goal for Arsenal.
"That was a great performance by us," said Ferguson. "We played really well. This is the time of the season we really need to kick on -- and it was an impressive result. We were sharp and incisive and could have scored more. But we are still behind Chelsea and I hope that Arsenal go there and batter them next Sunday!"
Chelsea leads United by a point and Arsenal by five points and has a game in hand on both teams. The Blues face Hull City Tuesday before hosting Arsenal.
"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."