Van Persie, 29, who ended an eight-year spell with the Gunners to join United in a £24 million ($39 million) deal in August, received plenty of abuse from the travelling supporters.
But he took fewer than three minutes to put United, now top of the table albeit Chelsea will regain first place if they win at Swansea later Saturday, ahead before refusing to celebrate in front of his former fans.
Wayne Rooney missed a penalty just before half-time -- his seventh miss in 20 attempts in the Premier League -- to leave United with a record of just one successful effort from their last five spot-kicks.
But France defender Evra doubled the advantage midway through the second half with his first goal at Old Trafford in almost two years before Arsenal midfielder Jack Wilshere, making just his second appearance after a long-term injury, was sent off after being shown a second yellow card.
Santi Cazorla curled in a late consolation goal for the Gunners but defeat left Arsenal, who haven't won a major trophy since 2005, nine points off top spot just 10 games into the league season.
While Arsenal remain bitter about van Persie's exit, his move to United has been an undoubted success, with his effort against his old team-mates, his eighth goal in the Premier League and tenth in 13 matches in all competitions.
The 29-year-old Dutch striker wasted no time in taking advantage of a Thomas Vermaelen error to score with his first touch.
Antonio Valencia flicked on Rio Ferdinand's pass to send Rafael clear down the right flank and although the Brazilian's cross was poor, Vermaelen failed to clear and van Persie struck a first-time finish from just outside the area.
Van Persie threatened once again midway through the opening period when he was picked out by a Rooney pass and out-paced Vermaelen, only to have his shot from a narrow angle saved by Vito Mannone.
David de Gea was finally forced into some work when Evra misjudged Bacary Sagna's long ball and Aaron Ramsey broke into the area before seeing his drive to the near post palmed away by the United goalkeeper.
Just before the break, Per Mertesacker had an anxious moment when his sliced clearance from Rooney's cross flew just past the top corner.
But the corner that followed led to Young's cross being handled by Cazorla, only for Rooney to send his penalty past the left post.
Just a minute after the restart, another Vermaelen error allowed van Persie through but the unmarked Valencia failed to even make contact with the Dutchman's cross eight yards from goal.
Michael Carrick also saw his drive fly narrowly wide after a Rafael effort was charged down.
As Arsenal pressed forward, Jonny Evans failed to make contact with a Santos cross and Olivier Giroud's effort glanced off the outside of the post.
Van Persie though beat the offside trap to latch on to Young's through-ball but saw his guided shot pushed just wide of goal by Mannone.
However, United did make the match safe when, from a short corner Rooney collected a return pass from Young and clipped in a cross that was headed in at the near post by Evra to make it 2-0.
United's task was made even easier when Wilshere, who was booked for an early challenge on Tom Cleverley, was sent off for a lunge at Evra.
Cazorla curled in from the edge of the area with the final kick but it was little consolation for Arsenal.
Source: AFP
Source: AFP