However, it was the visitors who would still break the deadlock after 27 minutes. Portuguese winger Nani exchanged passes with Darren Fletcher before firing into the bottom corner of the net from 20 yards out.
Striker Jonathan Walters also worked De Gea before the break, but the Spanish goalkeeper palmed his effort away from goal.
The home side's pressure finally told after 52 minutes. Matthew Etherington sent over a corner which was met by Peter Crouch and the England international headed in his first goal for Stoke.
United believed that they should have been awarded a penalty in the 69th minute when Ryan Shawcross handled Patrice Evra's shot, but the referee's assistant had already flagged for offside against substitute Michael Owen.
Another substitute, Ryan Giggs, had the chance to win the match for United in stoppage time, but he lifted his effort over the bar from four yards out.
Next up for United is a home match against Norwich City on Saturday, while Stoke travel to Swansea City a day later.