Starting a Premier League match for just the second time in 2017, Martial turned in an explosive performance down United's left flank, providing the assist for Juan Mata's opener before sealing a 2-0 win with a fine solo effort of his own.
The 21-year-old's excellent performance came following reports claiming Mourinho has given up on the France international. But the United boss paid tribute to his forward post-match, revealing he has "worked harder than ever" over the last two weeks when he has been out of the first-team picture.
"People sometimes forget that these teams like Watford and Stoke have very good players. I looked at this team and these players were in Italy when I was in Italy for Napoli, Inter, Lazio. These are top players," Mourinho told BBC Sport.
"In the first half the football was fabulous. The fans got behind the team just before we scored the goal because we were phenomenal. When I got the job they were saying at Manchester United you need to play the football in a certain way and I agree. You cannot play a counterattacking style, but then you have to analyse the situation.
"Martial deserves the chance. He has worked harder than ever in the last two weeks in the way I like - silence but hard."
United created a host of first-half chances before Mata finally broke the deadlock after 32 minutes. Martial's goal came 15 minutes into the second half before he was replaced by Marcus Rashford after 81 minutes. The former Monaco starlet received a standing ovation from those in attendance at Old Trafford and a warm embrace from his manager as he left the pitch.
United are now unbeaten in Premier League games, their best run of form since Sir Alex Ferguson left the club in 2013.