Robin van Persie scored against his former club as Manchester United defeated 10-man Arsenal.The home side were ahead minutes after kick-off as Van Persie capitalised on Thomas Vermaelen's poor clearance to stroke the ball into the far corner.Wayne Rooney fired a penalty wide before the break but the win was made safe when Patrice Evra headed home.Arsenal had Jack Wilshere sent off before Santi Cazorla scored a late consolation.Much of the build up to the game was unsurprisingly centred around Van Persie as he lined up against his former side for the first time since his summer move to United.Despite Arsene Wenger's call for respect to be shown to the Dutch striker, audible boos could be heard when his name was announced shortly before kick-off.But Van Persie responded to the taunts in perfect fashion.With barely three minutes on the clock, good work down the right between Antonio Valencia and Rafael saw the latter find himself in acres of space.The Brazilian delivered a low cross into the area which Vermaelen failed to clear and Van Persie took full advantage, directing a first-time effort into the far corner of the goal.The home side dominated after that with Arsenal looking largely toothless, and their inability in the final third was summed up when Olivier Giroud headed well wide from a corner midway through the half.United should have put themselves in a commanding position in first-half stoppage time when Cazorla was adjudged to have handled Ashley Young's cross inside the area, but Wayne Rooney fired wide from the resulting penalty.Valencia shot wide from five yards just after the break, but their dominance finally told in the 67th minute when Rooney crossed into the area for Evra and the Frenchman directed a header beyond Arsenal goalkeeper Vito Mannone.Arsenal had Wilshere sent off for a second bookable offence following a late tackle on Evra and they scored late on through Cazorla, but it was to be nothing more than a consolation.