The Frenchman struggled to have an influence during the early stages at Turf Moor, hounded out by claret shirts at almost every turn.
But Martial found a few yards of space in the 54th minute when Romelu Lukaku located him with a pin-point pass and the 22-year-old fired home past Nick Pope to hand Man United three points.
And Smalling, speaking after the game, revealed how Mourinho instructed his players to give Martial the chance to run at Bardsley at half-time.
“It was brilliant, he’s on fire at the minute,” he said.
“As soon as Bardsley was on a yellow card there, the instructions were just to give it to him the ball as early as we could because when he’s running at people he’s a danger.
“All year, him and Marcus have been playing on the left and, to be fair, both have chipped in with goals and assists. It’s great for us that we’ve got such a great attacking flair.”
This instruction from Mourinho played a crucial role in handing United their fourth win in a row since it meant that Lukaku, having broken away from a series of Burnley players, looked left immediately and found the winger in space.
And it continued to pay dividends as the game went on. The home side ramped up a gear going forward and United, in turn, had space to find Martial, who made life a nightmare for Bardsley at times during the latter stages and could have grabbed a second.