Eric Choupo - Moting scored twice as Stoke ended United's 100% league record in a topsy turvy tussle of fluctuating fortunes at the Bet365 Stadium.
The Reds had also yet to concede a goal, but the backline was finally breached as the Cameroonian international - signed from Schalke - put Mark Hughes' side ahead shortly before half-time.
United turned the game on its head through potent partnership Marcus Rashford and Romelu Lukaku, only to be pegged back once more by Choupo - Moting's second half leveller.
The Belgian striker squandered an excellent opening to win it, before Jack Butland's brilliant reaction save prevented a Kurt Zouma own goal in stoppage time.
The draw was enough to see United return to the top of the table, albeit only on goal difference following Manchester City's thumping win earlier in the day.
Butland showcased his England credentials throughout and - after Paul Pogba went close with a deflected effort - he was called into action on 25 minutes.
Eric Bailly's pinpoint pass played Rashford through, but his low drive was well blocked by the legs of the advancing keeper.
David de Gea twice saved well from Xherdan Shaqiri in quick succession, and Butland kept out Rashford with a fingertip stop in an increasingly end-to-end encounter.
Stoke looked to go in at half-time ahead, when Choupo - Moting slid in to score from close range after a low cross from the right.
United's riposte was almost instant, though, when Henrikh Mkhitaryan's corner was flicked on by Nemanja Matic, and Pogba's header hit Rashford to wrongfoot Butland on its way in.
Although a vibrant and lively Stoke side threatened to take the lead, it was United who moved ahead three minutes shy of the hour mark.
Mkhitaryan picked out Lukaku, whose initial effort was blocked, but he followed up to score at the second attempt to complete the turnaround.
As was the case with the hosts opener, though, United's joy proved short lived despite De Gea's best effort.
The Spaniard's stunning one-handed stop kept out Jese, but from the resultant corner, Choupo-Moting ghosted in unmarked at the far post to nod in his second.
Antonio Valencia had a shot deflected away and Lukaku fired over when well-placed as United upped the ante in search of a fourth successive league win.
It wasn't to be, but Stoke were indebted to Butland once more right at the end when his fine, instinctive save kept out Zouma's inadvertent effort.
A draw was ultimately a fair result from a entertaining - if frustrating - encounter that sees United edge back to the top of the table on goal difference.
Overall team performance: 6.5/10
United Faithful Man of the Match: Marcus Rashford