Radamel Falcao equalised for the visitors after former United trainee Ryan Shawcross had scored the first Premier League goal of 2015 in the second minute, but it was a third draw in four games for Louis van Gaal’s side.
United, who lost Ashley Young to an apparent hamstring injury, remain third, but could fall 12 points behind leaders Chelsea and nine points behind Manchester City if the top two win their games later on Thursday.
City entertain Sunderland at the Etihad Stadium, while Chelsea visit Tottenham Hotspur in the late kick-off.
Stoke caught United cold by taking the lead inside second minutes, with Shawcross volleying into the net from close range after Peter Crouch had helped on a corner.
Mame Biram Diouf, another United old boy, then spurned a glorious chance to extend Stoke’s lead when he bundled his way past Jonny Evans, only to curl wide with his left foot.
Falcao equalised in the 26th minute, hooking home left-footed at the back post after Wayne Rooney’s corner had been flicked on by Michael Carrick to register the third goal of his loan spell from Monaco.
Amid difficult, blustery conditions, both sides had chances to win the game, with Robin van Persie volleying narrowly wide for United and Crouch glancing a header against the post for Stoke.
Stoke also felt that they should have been awarded a penalty when a shot from Crouch struck Chris Smalling on the arm.
Elsewhere on Thursday, a place in the top four will be at stake at St Mary’s, where fourth-place Southampton entertain fifth-place Arsenal.
Freshly appointed West Bromwich Albion manager Tony Pulis will watch from the stands at Upton Park as his new club tackle West Ham United.
Managerless Crystal Palace visit Aston Villa, while Newcastle United, whose manager, Alan Pardew, will be absent after being given permission to speak to Palace about succeeding the sacked Neil Warnock, host Burnley.