A brace from Eric Maxim Choupo-Moting was enough to hold Jose Mourinho's men despite goals from strikers Marcus Rashford and Romelu Lukaku.
The result still leaves United at the summit of the Premier League but only clear on goal difference from Manchester City.
Question marks over Phil Jones and Mourinho's tactics
Despite a very good start to the season, Phil Jones has shown he still isn't fully dependable in the defence. A poor decision to gamble on a cut-back cost United the Stoke opener and poor marking of the Potters' number 10 let him slot in the equaliser, thus costing the Red Devils all three points.
Mourinho picked Ander Herrera over Juan Mata, in a move which made sense on paper. A midfield scrapper to help in a more physical battle with more defending to do. However, United were far less defensively secure than in the opening three games, often letting Mark Hughes' men in-behind, and were blunter in attack.
Lukaku and Darmian still have room for improvement
It has been a great start to his United career for Romelu Lukaku but he still has faults in his game. He needs to develop that utterly ruthless attitude a great Manchester United striker must possess. His late miss from close-range suggests he is not quite there yet but he certainly has potential.
When Matteo Darmian joined United in 2015, a fantastic start to the season led the majority of people to believe United had signed the real deal. However, that never really continued and he now finds himself an inconsistent starter and for good reason. A failure to get close to his man which allowed the cross for the first goal ultimately denied United the three points, and leave the fans calling for the return of Daley Blind.
David de Gea remains vital
Spanish goalkeeping superstar David de Gea carried the Red Devils through large parts of the post-Alex Ferguson era but he remains crucial under Jose Mourinho. He made some hugely important saves against Stoke and has pulled off some other stunners earlier in the year. Despite interest from Real Madrid, Mourinho must make it a top priority to keep hold of Spain's number one.