On his first appearance back at his former home since last summer's £24million move to Old Trafford, the Dutchman converted a penalty late in the first half to cancel out Theo Walcott's early opener.
Arsenal had given United a guard of honour before kick-off after Sir Alex Ferguson's team won the league on Monday and the gesture passed without any controversy despite all the pre-match speculation.
But that Van Persie was the man to equalise only added to the frustration of Arsenal's fans, who had booed their former hero throughout and ended the game aware they had missed a chance to open daylight over derby rivals Tottenham Hotspur in the battle for the top four.
Inevitably, with just two minutes on the clock, Van Persie was involved in the opening goal but it was not in the manner the 29-year-old would have hoped as he unwittingly helped his former club take the lead.
Slipping when attempting a cross-field pass on the halfway line, Van Persie gave Arsenal the ball before Tomas Rosicky was able to play in Walcott, who was allowed to finish despite appearing to be marginally offside when one-on-one with David de Gea.
With the title already secured, United were not doing much to dismiss suggestions they had little to act as motivation other than Chelsea's record points target of 95 but, in the 18th minute, Phil Jones wasted a good headed chance from Van Persie's left-wing cross.
Arsenal were the dominant force but they shot themselves in the foot in the 44th minute when Bacary Sagna, having made a mistake with a back-pass, brought down Van Persie for a penalty from which the Holland international rifled into the corner of the net.
After his title-winning hat-trick against Aston Villa on Monday, it was Van Persie's 25th goal of the season, which will surely see him win the Premier League's golden boot given the suspension of Liverpool's Luis Suarez.
As the second half began, Rosicky's curling effort with the outside of his boot went close to restoring Arsenal's lead but United responded, with Van Persie's low cross almost finding Wayne Rooney inside the six-yard box.
Shortly after the hour mark, and with United becoming the better team, Arsenal boss Arsene Wenger introduced star man Jack Wilshere in place of Rosicky among his second-half substitutes.
But other than a curler from Santi Cazorla, which had to be saved by De Gea, United remained the greater threat on the counter-attack and substitute Ryan Giggs saw a late effort deflected just wide as the game ended in a draw.
After the game, Ferguson was unimpressed with referee Phil Dowd, who booked five United players in comparison with three men from Arsenal.
The Scot told Sky Sports: "We have got probably the best disciplinary record in the country. For Manchester United to have five players booked, I do not think that is right."
But Wenger defended the aggression shown by his players, as he explained: "From the first to the last minute, it was two teams giving absolutely everything to win."