United manager David Moyes earned his first victory at Old Trafford but only after promoted Palace had midfielder Kagisho Dikgacoi sent off for a 43rd-minute foul on Ashley Young that proved to be the turning point in the match.
Van Persie slotted home the resulting penalty, even though the foul was committed outside the box, and Rooney — wearing a thick, black headband to cover a deep gash to his forehead sustained two weeks ago — completed an uninspiring win in the 81st minute.
"We could have done with scoring more goals," Moyes said. "But I thought we were dominant from the first whistle. I don't think the result was ever in doubt."
After a draw with Chelsea and defeat at Liverpool, the result at least got United back to winning ways after making its worst start to the season in five years. The introduction of Marouane Fellaini — a deadline-day signing from Everton for 27.5 million pounds ($43 million) — for his debut as a second-half substitute was also a welcome sight for the home fans, but there was little else to cheer.
Palace barely had a chance but United was far from fluent in front of former manager Alex Ferguson, who watched on from the directors' box to pile even more pressure on Moyes. And the groans were audible from United fans before the debatable refereeing decision by Jon Moss, which ruined the promoted visitors' hopes of taking anything back to London.
Young, who had already been booked for diving, fell easily under the challenge of Dikgacoi after seizing on a sloppy pass across the face of Palace's penalty area by Mile Jedinak. Not only was the challenge outside the area, there looked to be minimal contact on Young, who ran across the path of Dikgacoi.
"I literally can't afford it so I can't say a word (about the penalty decision)," said Palace manager Ian Holloway, who has already been fined this season for complaining about refereeing calls. "I'll let everyone else judge it."
With Palace's players still aggrieved and Dikgacoi already headed down the tunnel, Van Persie sent the goalkeeper the wrong way for his third goal of the season and the tension lifted around the stadium.
Fellaini was brought on for the ineffective Anderson in the 62nd minute and immediately made his presence felt in deep midfield, pepping up the hosts. But Palace coped pretty comfortably until Rooney curled a free kick into the bottom corner past the despairing dive of goalkeeper Julian Speroni.
Rooney missed England's two recent World Cup qualifiers with a head injury sustained in a training-ground collision but returned to action here and waved to the crowd after grabbing his first goal of the season, indicating all is well after a summer of upheaval when he was linked with a move to Chelsea.
"It looks like a sumo wrestler's headband," Moyes said, laughing. "He tired a bit in the second half but I thought he was great in everything that he did. I wanted him to get 90 minutes under his belt which is important with the busy week we have coming up."
Moyes said he would speak with Young after his booking for simulation, a decision the Scottish coach agreed with.