In the English Premier League match at a rainy Old Trafford, full-back Antonio Valencia blasted Manchester United into a ninth minute lead.
He had cut inside on to his unfavoured — but still potent — left foot before scoring.
Anthony Martial and Romelu Lukaku later wrapped up the victory for Jose Mourinho’s side.
The result leaves second-placed United 12 points behind leaders Manchester City who suffered their first league defeat this season in a thrilling 4-3 reverse at Liverpool on Sunday.
Stoke’s new manager Paul Lambert, appointed earlier on Monday to replace the recently-sacked Mark Hughes, watched from the stands as Valencia put United ahead.
Stoke’s Stephen Ireland, making his first start since May 2016, then missed two good chances as the visitors showed plenty of attacking intent.
But seven minutes before the interval, United’s French winger Martial made it 2-0 with a sweet first-time finish after being set up by Paul Pogba.
Lukaku rounded off the win with a 72nd minute goal, wriggling to find enough space for a shot into the bottom corner after good work from Martial.
Mourinho omitted winger Henrikh Mkhitaryan from the squad amid reports that Arsenal were interested in taking him to The Emirates as part of a swap deal for their Chile forward Sanchez.