Yet the performance of skipper Nemanja Vidic was equally notable, as he guided United to only their fourth Premier League clean sheet of the season after Gareth McAuley's early own goal had put the hosts in front against West Brom.
And when Van Persie curled home a brilliant effort in the final minute, the Red Devils' seven-point lead at the top was preserved.
United got their noses in front courtesy of McAuley, who could only divert a bullet cross from Ashley Young into his own net but it should have been more.
Vidic was wide with a couple of headers and Gabriel Tamas turned away Michael Carrick's goalbound shot.
The nearest United went to doubling their lead was when Young strode onto a deflected Antonio Valencia cross. He hit it sweetly on the half volley, only for former Red Devils keeper Ben Foster to respond with a brilliant save, which earned his slice of good fortune when he shoved the ball onto the crossbar and over.
Young completely miskicked when Valencia's cross presented a golden opportunity on the hour, which offered a Baggies outfit already growing in self-belief more reason for optimism.
Had Chris Brunt's piledriver been either side of David de Gea it surely would have brought the visitors level. As it was, the shot went straight to the Spain keeper.
Vidic needed to be in the right place to clear a Romelu Lukaku cross that threatened panic inside the United six-yard box and the sight of his fellow defenders throwing themselves at anything that moved, it had turned into an unedifying backs-to-the-wall effort so unlike the thrill-a-minute action this stadium has become used to.
Van Persie was denied by Foster with nine minutes remaining but the former England keeper could do nothing about the Dutchman's late shot, which curled expertly into the top corner from Paul Scholes' pass.
Source: PA
Source: PA