Mourinho left Armenian winger Henrikh Mkhitaryan out of the squad amid reports that Arsenal were interested in him as part of a swap deal for Chile forward Sanchez, who is no longer a target for Manchester City, according to British media reports.
In the ninth minute, United nosed ahead when skipper Valencia blasted cut inside on to his left foot to hammer into the far corner, well beyond the reach of visiting keeper Jack Butland.
Paul Lambert, Stoke's new manager, watched from the stands, with the sacked Mark Hughes' former assistant Eddie Niedzwiecki in charge of the team.
There was a passage of play when Stoke attacked but there was no real threat to home goalkeeper David De Gea.
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 who was brilliant on the night.
On the cusp of halftime, Stoke's Swiss attacking midfielder Xherdan Shaqiri tested keeper De Gea with a low drive.
It was all United after the break but despite a flurry of chances, they could not extend their lead and arguably put the match to bed until the 72nd minute. Lukaku showed enough power to hold off his marker and shoot into the bottom corner after good work from Martial.
"Stoke bought players to play football, they were not afraid to play and they created us problems in the first half," said Mourinho after the match.
Niedzwiecki said he was unclear whether he would remain at the club once former Norwich City and Aston Villa boss Lambert set up his own staff.
"Paul Lambert said a few words to the players in the hotel before the game but he showed me the respect, it was my team today. I enjoyed the experience but it has been incredibly difficult personally," he said.
"I will find out my future in the next 48 hours. I know how the game works."
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