The result leaves David Moyes' men seventh in the Premier League, with fourth-placed Liverpool able to open up a nine-point gap over them if they beat West Brom on Sunday.
On a day where none of the top four sides played and Tottenham dropped points, United failed to take advantage, going down to an organised Stoke side at the Britannia Stadium.
In a first half largely dominated by United, Stoke went ahead after 38 minutes thanks to a deflected Adam free kick. The former Liverpool midfielder's effort hit Michael Carrick on the edge of the area, taking the ball beyond the reach of a helpless David de Gea.
United were level just two minutes after the break, however, Robin van Persie the man on target as he became the first player in Premier League history to score in eight successive appearances against a single opponent.
But the visitors' celebrations were cut short when Adam unleashed an unstoppable effort past De Gea from outside the area after 52 minutes. It proved to be the winner as United lost their eighth league game of the season and their third straight match on the road in all competitions.
United boss Moyes started the attacking trio of Juan Mata, Van Persie and Wayne Rooney together for the first time as they looked to claim a third victory over Stoke this season.
While United were able to field a full-strength forward line, Moyes was given a defensive injury headache just 10 minutes in when Jonny Evans was replaced by Rafael Da Silva having suffered what appeared to be a hamstring problem.
Rooney then had the first chance of the game, turning and firing wide inside the area after 14 minutes following Patrice Evra's cross from the left.
And from there, United began to pile on the pressure, Van Persie being next to go close with an effort that deflected wide past Asmir Begovic's right-hand post.
However, Stoke survived the strong United spell and perhaps should have engineered a shot on goal when Jonathan Walters was slow to react to a loose ball on the edge of the box - Phil Jones producing a well-timed tackle.
Van Persie then went close for the visitors when his close-range header took a deflection off Glenn Whelan and crept over the crossbar.
But seven minutes before the break, Adam's free kick, with the help of a large slice of luck and an inadvertent Carrick deflection, put the home side ahead.
And things got even worse for United before half-time, when Jones was taken off injured after a clash of heads in the air with Walters.
Yet Van Persie was again the man to haunt Stoke as he angled a finish past Begovic following Mata's carefully-weighted through ball.
The scores were level for just five minutes, though, as Adam registered his sixth league goal of the season with a magnificent left-footed strike.
And Stoke, who were in the relegation zone prior to kick-off, held on to move 11th in the table with their first league win since December.
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