Sir Alex was fuming when ex-Red Ryan Shawcross escaped punishment for blatantly wrestling Hernandez to the ground as the home side's strong-arm tactics sometimes crossed the line. Rooney had a chance to score seconds later but his free-kick flew inches wide of Begovic's right-hand post.
Stoke managed to mount some pressure in first-half injury time but a similar pattern emerged after the interval with United in control, without really ramming home the advantage. Superb passes by Rooney and Hernandez carved out an opportunity for van Persie but the Dutchman lashed into the side-netting from a difficult angle.
As the Potters became more comfortable in defence, they tried getting the ball forward quickly and started to muster attempts of their own. Jon Walters hooked over the bar and Adam worked David De Gea with a couple of wind-assisted shots. Kenwyne Jones then blazed off target but the warning signs were soon heeded by the Reds.
Phil Jones and Antonio Valencia worked the ball cleverly down the right and Rooney bided his time before releasing van Persie. Andy Wilkinson made a reckless tackle as van Persie dummied back and, ultimately, floored United's leading goalscorer inside the area to prompt referee Jon Moss to point to the spot. Calmly ignoring the fact that the wind initially blew the ball from the spot, van Persie stepped up to place his penalty wide of Begovic before sprinting off to celebrate with Sir Alex, Rene Meulensteen and Alexander Büttner on the sidelines.
The second goal led to unrest among sections of the home support but City's response on the pitch was more impressive with De Gea forced to smother a shot by Ryan Shotton following a slip by Evra, which could have proved costly. Kenwyne Jones then tumbled over a grounded Nemanja Vidic inside the area but, despite the appeals, a spot-kick would have been