Manchester City temporarily led the standings after winning their lunchtime kick-off 2-0 against Everton at the Etihad Stadium, but United went back to the summit despite only drawing their evening game at the Britannia Stadium.
United and City both have 16 points from six matches with last season's champions ahead on goal difference.
United led at Stoke with a first half goal from Nani but were pegged back when Peter Crouch headed home a corner.
United, who had won all six league matches between the sides since Stoke gained promotion to the Premier League in 2008, took the lead with a well-struck drive from Nani after 27 minutes.
Stoke equalised with a Crouch header, his first goal for the club.
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