Since leaving the Emirates last year, van Persie has never failed to score against his ex-employers and he made that three games in succession as he bagged the winner for United.
He rose to meet a Wayne Rooney corner on 27 minutes to give David Moyes a much needed win on another amazing weekend, in which Chelsea's home draw on Saturday was followed within 24 hours by shock defeats for Tottenham and Manchester City. United have now closed to within five points of Arsenal, who suffered their first league defeat since the opening day of the season.
Indeed, six points now separate the first eight in the table, with Liverpool and Southampton now Arsenal's closest pursuers.
Quite apart from van Persie's goal, Rooney ran himself to a standstill and Phil Jones was immense, initially in midfield, then in central defence following the departure of Nemanja Vidic with a head injury.
The opening 25 minutes had been played out in midfield, with neither side able or seemingly willing to get hold of the game.
A rare deflected effort from Rooney had showed his willingness and he played a big part in the breakthrough just before the half-hour.
Rooney made some space on the left and sent over a wicked cross that Thomas Vermaelen could only head over his own bar for a corner.
Rooney then took the resulting corner which saw van Persie leap above Olivier Giroud and glance the ball into the top corner to give United the lead.
Missing Per Mertesacker due to a virus that was also affecting Mikel Arteta, the Gunners lacked the zip that has taken them clear at the Premier League summit.
Only Mathieu Flamini escaped the malaise, and he was booked for a late tackle on the influential Jones.
The young England star was one of United's stand-out performers, driving out of midfield in a manner so obviously lacking for the past three seasons.
He was also at the centre of the first of two worrying head clashes. Cautioned when he clattered into Wojciech Szczesny, TV replays showed the contact to be accidental.
For a few seconds, the Arsenal keeper did not move. After treatment, Szczesny continued, as did Jones, who had moved away rubbing his head.
Nevertheless, given the recent furore over Hugo Lloris over the last week, the decision raised an eyebrow.
Then just before the break and another head injury came as United suffered a huge blow when Vidic left dazed after a clash with his own keeper David De Gea and that meant he did not return after the break.
Tom Cleverley was the man brought on ahead of Marouane Fellaini to replace Vidic, which meant a tweaking of United's side with Jones - who had impressed in central midfield - dropping back to partner Jonny Evans.
Arsenal pushed hard at the start of the second-half, but on the hour again Rooney was at the heart of everything and he should have doubled the lead.
A Shinji Kagawa flick-on came to Rooney via van Persie, but with the goal at his mercy he sent his left-footed shot wide.
With that Jack Wilshere was introduced by Arsenal as they looked to push for the equaliser, but United defended valiantly.
Chris Smalling was involved in key moments at both ends before Sagna's low cross bounced inches away from Nicklas Bendtner - but the game was United's, who were inspired by Rooney.