David Moyes' first league match in charge of United couldn't have gone any better, with Van Persie matching Danny Welbeck's brace with two brilliant goals of his own to signal his intent on finishing top scorer in England for a third straight season.
There is already an air of discontent at Arsenal, however, after a 3-1 home loss to Aston Villa, which ended with fans booing the team off and voicing their anger at manager Arsene Wenger's failure to strengthen his threadbare squad in the close season.
Christian Benteke scored twice for Villa, with Laurent Koscielny's second-half sending-off after two yellow cards compounding Arsenal's misery.
Liverpool relied on Daniel Sturridge's first-half goal and a late penalty save by debutant Simon Mignolet to clinch a 1-0 victory against Stoke, while West Ham, Southampton and Fulham also opened an eagerly anticipated campaign with wins. Norwich drew 2-2 with Everton.
After securing his first piece of silverware at United by winning the Community Shield last weekend, Moyes now has a maiden league victory to savour. Suddenly, the pressure of filling the boots of predecessor Alex Ferguson, who won 38 major titles in nearly 27 years at Old Trafford before retiring in May, doesn't feel so heavy.
"It's one game in 38 and, from that point of view, it's just the start for me," Moyes said.
It helps having someone like Van Persie in your team.
The Netherlands striker was the main reason why United was able to reclaim the league title from Manchester City last season and he has picked up where he left off, putting United ahead with an acrobatic volley in the 34th minute and then virtually sealing victory in the 72nd by smashing a 20-yarder into the top corner.
With Welbeck also weighing in with two goals — the second a deft chip in injury time — it justified Moyes' decision to leave unsettled striker Wayne Rooney on the bench until the 61st minute. Rooney, who has been pushing for a move away from United, received a generous welcome by the travelling support when he entered and set up Welbeck's second goal in a sharp cameo.
Wilfried Bony's debut goal for Swansea made it 3-1 but Swansea faded after a bright start, with its defence unable to cope with the movement of Van Persie and Welbeck.
As with United, it's a case of new season, same old story for Arsenal.
Wenger's team is unlikely to be challenging for the title this season unless the club, which is awash with cash, can recruit some marquee names to add to a squad that the French manager acknowledged on Friday was light on numbers. Wenger was hit with chants including "You don't know what you're doing" and "Spend some (expletive) money" minutes as the final whistle approached against Villa.
"My job is to make the fans happy, but we haven't lost a game because of that (not spending)," Wenger said. "We are ready to spend, but until we buy players we have to win football games and it is not an excuse not to win the game today."
Olivier Giroud gave Arsenal the lead in the sixth minute but Benteke, who put in and then withdrew a transfer request over the summer, equalized in the 22nd when he headed home a rebound after his penalty was saved by goalkeeper Wojciech Szczesny.
The Belgium striker then converted a 66th-minute penalty following Koscielny's clumsy foul on Gabriel Agbonlahor, earning the defender a first yellow card, and debutant Antonio Luna sealed the points in the 85th for Villa by racing clear on the break to score in the bottom corner.
It was a much more positive start to the campaign by Liverpool, who dominated against Stoke but only had Sturridge's 25-yard strike to show for its efforts.
That profligacy almost cost them when Daniel Agger handballed in the area in the 88th minute but Mignolet ended a nervy debut by clawing away Jon Walters' spot kick and then denying Kenwyne Jones' effort on the rebound.
Luis Suarez, who was serving the fifth match of a 10-game ban for biting an opponent last season, was cheered by some fans as he walked the perimeter of the Anfield pitch with his daughter before kickoff despite an off-season dominated by transfer speculation surrounding the striker. He watched the match from an executive box high up in the stands.
The scorer of England's winner over Scotland on Wednesday on his international debut, Rickie Lambert completed the perfect week by converting a last-minute penalty for Southampton in a 1-0 victory at West Bromwich Albion.
Goals either side of the break by Joe Cole and Kevin Nolan were enough for West Ham in a 2-0 home win over promoted Cardiff and Pajtim Kasami grabbed a 52nd-minute winner for Fulham in a 1-0 victory at Paolo Di Canio's Sunderland.
Norwich went ahead at Carrow Road through Steven Whittaker before goals by Ross Barkley and Seamus Coleman in a five-minute span gave Everton the lead by the 65th minute. Van Wolfswinkel levelled in the 71st.