Elsewhere, Everton were held to a 2-2 draw by Fulham and Chelsea were unable to beat Swansea, while Sunderland and Stoke City lost to Aston Villa and Norwich City.
In the late kick-off at Upton Park, Manchester City could only manage a goalless draw against West Ham United.
Here is the best of the reaction from the professionals to Saturday’s results on Twitter.
Manchester United defender Rio Ferdinand (@rioferdy5) praises Van Persie for a mature celebration: “RVP goal celebration was respectful to the AFC fans #fact! The #AFC fans who hurled abuse at him in the stadium were not!”
Red Devils legend Peter Schmeichel (@Pschmeichel1) is still worried by United’s defending: “Three points and a relatively easy ride are the positives, but why can we not keep it tight at the back…?!!!”
Celebrity Arsenal fan Piers Morgan (@piersmorgan) is disgusted by Andre Santos swapping shirts with Van Persie at half-time: “If Ferguson had seen his worst performing United player swap shirts with someone at half-time, he’d drop him forever. Wenger’s lost his edge.”
Everton midfielder Marouane Fellaini (@fellainiM) thanks the travelling Toffees for their support: “Thank you for your support… We’ll work again …”
John Heitinga (@Johnheitinga) felt Everton merited three points: “#Everton unlucky. The better team against #Fulham away but only one point: 2-2. Thanks for your support #greatfans!”
Tottenham midfielder Mousa Dembélé (@mousadembele) is disappointed to see Spurs lose: “Gutted we lost today, hope we will take home the points next week! For those who have asked about my injury. Not sure when I’ll be back, still in process.. Working hard!”
Sunderland striker Louis Saha (@louissaha08) is frustrated to lose to Aston Villa: “I’m not happy at all with us losing today. Missed a good header but keep working!”
Stoke midfielder Charlie Adam (@Charlie26Adam) feels much the same about a 1-0 defeat by Norwich City: “Gutted about result. Created some chances. Great support and a big match next week against QPR!”
Potters goalkeeper Asmir Begovic (@asmir1) felt Stoke deserved more: “I can’t believe we lost today. Great effort again today but no luck again for us. The support was great, making the long trip!#potternation”
Swansea midfielder Wayne Routledge (@WayneRoutledge) is pleased with a point against the reigning European champions: “Great point, fully deserved too! Great support to the end and beyond, enjoy your weekend…”
Manchester City striker Sergio Aguero (@aguerosergiokun) eyes a big game against Ajax on Tuesday: “We wanted the win, it didn’t happen – but we’re still in the race. Got to prepare for Tuesday’s decisive match against Ajax.”
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