The French forward, who reportedly rejected the club's offer of a contract extension this week, won the penalty for Paul Pogba's opener and curled in a splendid goal of his own after half-time.
The 25-year-old scored with a fortuitous follow-up after Jordan Pickford saved his initial attempt from the spot midway through the first half at Old Trafford.
Martial started the game as bright as ever, beating his marker time and again as he set up Juan Mata for a free header before winning the penalty that put United 1-0 up.
But a relieved Mourinho praised Pogba after the game for having the mental strength to take the 27th minute penalty.
Mourinho said: "The thing I like is the desire to take it".
Sigurdsson made no mistake with an assured penalty and Silva played the remainder of his cards by throwing Cenk Tosun and Dominic Calvert-Lewin on for Gueye and the disappointing Walcott.
"Paul wants to take and that for me is fantastic". I think he can, I think the goalkeepers don't move and they are waiting for his decision so I think he probably has to learn from that.
'In terms of my approach to my young players, that's the way I am.
"That moment makes it easy for our opponents".
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The Prime Minister also said that the government was in contact with two other friendly countries for more financial assistance. Pakistani Finance Minister Asad Umar has estimated the country needs around $12 billions to meet its immediate liabilities.
Someone on social media pointed out that Pogba's little trot from start to finish took more time than Jamaican sprinter Usain Bolt takes to run 100m.
The youngster missed a one-on-one in the second half after being sent through by Mata and was finally put out of his misery in the 64th minute as Lukaku was brought into the game for the man brought in to replace him, not doing particularly better though as he too, spurned a clear header to seal the game for United.
United were still in the ascendancy but their attacks were being interspersed by concerning moments at the back, with Seamus Coleman fizzing over under pressure.
Mourinho and Martial have fallen out on more than one occasion during their time together, but the United manager has suggested that it is the Frenchman's camp who are at fault for the player's inconsistent performances. We needed points. I think in the last game against Chelsea we should have won.
The visitors were looking shaky towards the end of the half and United probably felt they could have went into the break with at least a two-goal cushion. "But I always feel that every game is the game [that he will score]". And to score goals is really hard for us - you can see that in this moment.
Pogba scored his first Premier League goal since August in rather controversial fashion.
'He took quite a long time to understand what we want, quite a long time for his brain and body to be ready for how we want him to play, ' Mourinho added.
"We played well in some moments of the game".