The Dutchman's penalty was quickly followed by an unstoppable volley from his strike partner to break down the resilient hosts, and the goals were a relief for the Reds after spells of persistent possession play had failed to reap rewards.
Palace soaked up waves of United pressure in the first half, with Rooney's curling effort from the edge of the box headed away from under his crossbar by Damien Delaney, while Nemanja Vidic headed the rebound just over. David De Gea was largely untested but he was alert enough to parry away a deflection off Chris Smalling, while Marouane Fellaini wasted an opportunity just before the break when the Belgian, back in the side for the first time since 4 December, shot wide after a neat touch from Juan Mata.
Palace went on the attack early in the second half, but the game changed on 62 minutes when a clumsy challenge by Eagles striker Marouane Chamakh on Patrice Evra on the edge of the box resulted in a penalty that van Persie clinically despatched. A curling shot from Cameron Jerome drew a save from De Gea low to his left, and this proved to be vital shortly afterwards when Evra cut the ball back to Rooney, who lashed in a superb volley from just inside the area.
Van Persie struck the bar as United strived to kill the game off, and De Gea was in action again when he denied Yannick Bolasie, but United saw the game out comfortably to claim three points and move into sixth place.