Chelsea was held to a 1-1 draw at Swansea after conceding an 88th-minute equalizer to Spanish winger Pablo Hernandez, falling a point behind United after 10 games.
Manchester City could have joined United in leapfrogging the European champions but stayed third after failing to turn dominance into goals in a frustrating 0-0 draw at West Ham.
United is the form team of the three expected title contenders, and in Van Persie it now has the league's top scorer after the Dutchman grabbed his eighth goal of the campaign to set the hosts on their way to a comfortable win at Old Trafford.
Van Persie's low drive in the third minute, after poor defending by Thomas Vermaelen, was added to by Patrice Evra in the 67th, meaning United wasn't forced to pay for Wayne Rooney's missed penalty in first-half injury time.
"It's the first time I've ever played against a former club, so it's a special day," said Van Persie, who refused to celebrate his goal against the side that sold him for 24 million pounds ($38 million) in August.
Everton conceded in the last minute in a 2-2 draw at Fulham but climbed a place to fourth above Tottenham, which was jeered off after surprisingly losing 1-0 at home to Wigan.
Norwich and Aston Villa moved clear of the bottom three by grinding out 1-0 victories, against Stoke and Sunderland respectively.
Van Persie has settled seamlessly into the United team and he showed his old employers just what they are missing this season, shooting low into the corner after Vermaelen fluffed his clearance.
He could have added more goals against an Arsenal team that lacked urgency and pace and looks far from the side that used to regularly contend for titles with United and Chelsea.
Jack Wilshere, playing his second game back after 17 months out injured, was sent off for Arsenal two minutes after Evra's goal for picking up a second booking. The visitors managed a stoppage-time consolation through Santi Cazorla, who handled the ball to concede the penalty to United, but Arsenal remained sixth on 15 points — the team's worst start to a Premier league season since Arsene Wenger joined in 1996.
"We had a lot of the ball, but we were not very efficient in our final third or in their final third," Wenger said. "Then you feel the domination was a bit illusionary — they created more chances and deserved to win the game."
Chelsea hasn't been headed in the league since Aug. 22, but Hernandez's low strike means the team has won just one of its last four matches in all competitions.
After two straight draining matches against United — a 3-2 loss in the league and a 5-4 extra-time win in the League Cup — Chelsea lacked spark, especially with Juan Mata out injured and captain John Terry serving the final match of his four-game suspension for racially abusing an opponent.
Victor Moses' 66th-minute goal was one of the few clear-cut chances they created.
"Mentally and physically, it was very demanding playing two times against United," said Chelsea manager Roberto di Matteo. "When you are so close to winning away from home, you are always disappointed."
City, which is a point behind Chelsea, failed to score in a match for the first time since December last year and could even have lost the match had Kevin Nolan's fourth-minute volley not been ruled out for a dubious offside decision.
The defending champions now face a must-win game against Ajax in the Champions League on Tuesday but aren't the same force as last season.
Tottenham lost touch with the leaders by slumping to a lacklustre loss to Wigan, leading to the home supporters venting their anger toward the team and manager Andre Villas-Boas.
Ben Watson scored the winner in the 56th minute for Wigan, which could easily have won by a bigger margin. Having lost to Chelsea in the league two weeks ago, Spurs have lost back-to-back Premier League games at White Hart Lane for the first time in four years and is nine points off United.
"The performance was more pleasing than the result today," Wigan manager Roberto Martinez said. "It was a perfect performance."
Steve Sidwell scored Fulham's last-gasp equalizer against Everton, pegging the visitors back after a double from Marouane Fellaini had helped them recover from conceding an early own goal by goalkeeper Tim Howard.
"It feels like a defeat ... we're as sick as it gets," Everton manager David Moyes said.
Bradley Johnson grabbed Norwich's winner at home to Stoke, extending the team's unbeaten run to three matches, and Gabriel Agbonlahor was Villa's scorer at Sunderland.