Despite United manager David Moyes starting with Robin van Persie, Wayne Rooney and record signing Juan Mata together for the first time, the champions suffered their eighth Premier League defeat of the season at a windswept Britannia Stadium.
Moyes could curse his luck after injuries to Jonny Evans and Phil Jones and a fortunate opener for Stoke, but another below-par display saw his side lose further ground on their top-four rivals.
Van Persie led the line with Rooney behind him, flanked either side by Mata and Ashley Young, but they saw little of the ball in the opening exchanges.
Stoke started promisingly, but Peter Crouch’s attempted bicycle kick failed to come off after a good cross from Jonathan Walters.
Moyes opted for Chris Smalling at right-back instead of Brazilian Rafael da Silva in a move designed to help United’s defence deal with Stoke’s aerial threat, but that plan was scuppered 11 minutes into the game.
Evans picked up an injury and Smalling was forced into the centre, with Rafael called on from the bench.
United finally settled as Mata got his first touches and Rooney had the first real chance for the visitors when he lashed a half-volley into the ground and just wide of the post from Young’s cross.
The champions started to put some pressure on the Stoke defence, but clear-cut chances were at a premium.
Stoke had opportunities to create openings, but they were wasteful in the final third until they got a massive stroke of luck in the 38th minute.
Adam struck a speculative free-kick from 35 yards that looked set to fly wide, only for it to hit the knee of Michael Carrick and ricochet in the opposite direction, leaving United goalkeeper David De Gea rooted to the spot.
United went on the attack straight from the kick-off, but goalkeeper Asmir Begovic got down well to repel Tom Cleverley’s long-range effort.
It got worse for Moyes and United before the break when Jones was carried off on a stretcher after a nasty clash of heads with Walters.
United’s luck appeared to be changing shortly after the restart. Marc Wilson made a mess of a routine clearance and it fell to Mata, who coolly picked out Van Persie for the Dutchman to curl in an equaliser.
But Stoke responded, and if Adam’s first goal had been fortunate, his second was anything but.
Walters’s knock-down was missed by Marko Arnautovic, but Adam ran onto it to launch a powerful effort from outside the box that flew into the top-right corner.
United pushed for another equaliser, but Mata hesitated in the area when presented with a chance before Arnautovic curled wide at the other end as Stoke counter-attacked.
After a period of United pressure, substitute Oussama Assaidi came close to putting the game beyond doubt, but De Gea tipped his strike over.
Patrice Evra headed wide late on, while Tom Cleverley lashed a rebound over the bar in stoppage time after Begovic brilliantly pushed a free-kick from Rooney onto the post.
However, former United striker Mark Hughes saw his Stoke side hold on for a first victory over the men from Old Trafford since 1984.
With fourth-place Liverpool visiting West Bromwich Albion on Sunday, United could now find themselves nine points outside the Champions League places with just 14 games to go before the weekend is out.