Ryan Shawcross opened the scoring early on, only for Radamel Falcao to equalise midway through the first half, and while both teams had opportunities, neither could force a winner.
The draw extends United’s unbeaten run to 10 Premier League matches, but they were made to battle for the point in a keenly-fought contest.
The home side started strongly in the windy conditions and forced the opening goal inside two minutes after Steven N’Zonzi won a corner on the right flank.
Peter Crouch escaped his marker with ease and had a free header from deep that was helped into the net by Shawcross from close range against his former club.
The United back three, featuring Jonny Evans, Phil Jones and Chris Smalling together for the first time this season, looked particularly uncomfortable and Evans was almost caught out soon after.
After allowing the ball to bounce, the defender surrendered possession to Mame Biram Diouf and the Stoke striker got free, only to miscue his left-footed shot when one-on-one with David de Gea.
United succeeded in getting their passing game going after these early scares and were rewarded with an equaliser courtesy of the industrious Falcao.
Wayne Rooney’s corner was flicked on by Michael Carrick and the Colombian striker was quickest to react in guiding the ball low into the far corner of the net with his left foot.
United had another warning soon after, when Geoff Cameron headed wide from Marko Arnautovic’s free-kick, but opportunities from open play were at a premium.
United dominated the early part of the second half without creating much as Stoke, who were playing with confidence having won their previous two games, seemed content to play on the counter-attack.
One of those advances saw Jones head wide of his own post with Crouch lurking, before Smalling was fortunate to get away with a strong shout for handball from the subsequent corner.
The incident seemed to lift the home team and they pushed on again, with Crouch hitting the far post with a flicked header from another Arnautovic free-kick, before Diouf also went close.
United, who lost Ashley Young to a hamstring injury in the second half, did go close through Robin van Persie but rarely looked to have enough to find a breakthrough of their own.
As a result, the two teams were forced to settle for a point apiece, with both taking some comfort from the fact that they succeeded in extending their unbeaten runs.
Stoke City: Begovic (6), Cameron (6), Shawcross (7), Muniesa (6), Pieters (6), Walters (6), N’Zonzi (6), Whelan (6), Arnautovic (7), Crouch (7), Diouf (6).
Subs: Assaidi (6).
Man Utd: De Gea (6), Smalling (5), Jones (6), Evans (5), Young (6), Carrick (6), Mata (6), Shaw (6), Rooney (6), Falcao (7), Van Persie (6).
Subs: Herrera (6), Januzaj (6), Rafael (6).
Man of the match: Ryan Shawcross.