Louis van Gaal's side had to bounce back from the shock of falling behind to a second-minute goal from former defender Ryan Shawcross at the Britannia Stadium.
And they had to show great resilience to stretch their unbeaten run to 10 matches after Radamel Falcao had got them back on level terms with an opportunistic goal.
United may look back on this as a point gained rather than two dropped at a windswept stadium where the home side tend to make things uncomfortable for visitors.
Despite the fact that Stoke were robbed of their main attacking threat, Bojan Krkic, who was ruled out through injury, Mark Hughes's men quickly imposed themselves on the game.
Peter Crouch was picked out at the far post by Marko Arnautovic's deep ball into the box and his goal-bound header was hooked into the roof of the net by the grateful Shawcross.
Although United composed themselves after the early shock by claiming the lion's share of possession, their final ball often let them down.
The fragile nature of United's defending was exposed again when their former striker Mame Biram Diouf outmuscled a hesitant Jonny Evans, only to shape his left-foot shot wide of the left-hand upright.
It proved to be a decisive moment in the contest because rather than finding themselves two goals down, United were back on level terms seven minutes later.
Like Stoke had done in the second minute, United secured their equaliser by way of a well-worked corner.
Michael Carrick got the faintest of touches to Rooney's delivery from the left-hand side and the ever-alert Falcao finished with style from close range.
Neither side managed to carve out another clear-cut chance before half-time, although Falcao's control let him down at a crucial moment when he threatened to break onto a through-ball from Ashley Young.
United's best moment of the half came when when Van Persie instinctively brought down Juan Mata's chipped ball on his chest and sent a delicate lob over the stranded Asmir Begovic but inches wide of the far post.
Stoke pressed hard for a winner, while Young was forced off with an apparent hamstring injury, but Van Gaal's side held firm to claim a point that consolidated their top-four position.
Like Sports on Facebook, follow @ETribuneSports on Twitter to stay informed and join in the conversation.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ