The Colombia international leveled things up midway through the first half after Ryan Shawcross struck against his former club to give the Potters the lead early on.
Radamel Falcao's third United goal earned a share of the spoils from an encounter affected by heavy winds after Ryan Shawcross had given Stoke an early lead at the Britannia Stadium.
Stoke headed into the clash having won back-to-back games over the festive period and, despite star man Bojan being unavailable due to a hamstring injury, the feel-good factor remained for the home side as Shawcross opened the scoring in the second minute.
Louis van Gaal's men came back into the game, however, and went into the break level thanks to Falcao.
The second half did not bring any other goals, although Stoke ended the game having been denied a clear penalty for a Chris Smalling handball and seen Peter Crouch rattle the woodwork.
Stoke could not have enjoyed a better start as the club went in front almost immediately courtesy of its captain.
A well-worked Marko Arnautovic corner to the back post found Crouch, who nodded down for former United man Shawcross to side-foot a volley home.
The visiting side came back into the game thereafter, although clear-cut chances were not initially forthcoming.
Stoke could easily have been further behind when Jonny Evans failed to deal with a long ball, gifting Mame Biram Diouf a golden chance that he somehow curled wide.
Stoke was left to rue that missed opportunity even more in the 26th minute as United equalized.
Again it was a set piece that proved critical, with Michael Carrick flicking on Wayne Rooney's corner for Falcao to cleverly sweep home despite an awkward bounce.
That continued to look the most likely route for another goal, with typically blustery winds at the Britannia creating issues for both sides.
Those conditions were hardly befitting of a footballing spectacle, illustrated by the teams struggling for fluency.
United began to take control around the hour mark, yet Stoke was unfortunate not to be given a penalty when Smalling handled Crouch's header.
Van Gaal's side almost took full advantage of that letoff when Juan Mata chipped into Robin van Persie, who followed fine chest control by flicking a superb effort with the outside of his foot wide.
The side was still vulnerable from set pieces, however, epitomised by Crouch heading another Arnautovic delivery against the post.
Diouf was next to threaten, seeing his powerful, deflected volley fly wide as United failed to deal with another dangerous corner.
United came on strong towards the end of game, even if the best chance fell to Stoke when Oussama Assaidi hit straight at David de Gea.
But both sides were left to settle for a point in the Premier League's opening match of 2015..