Two first-half goals from Martial sealed the victory in the first behind-closed-doors fixture at Old Trafford before he added the third late on to become the first Manchester United player to score a hat trick in the Premier League since Robin van Persie in April 2013.
Martial turned in from close-range at the near post from Marcus Rashford's drilled low cross from the right after seven minutes, the earliest scored in a Premier League game since it resumed earlier this month.
And he added a second in the 44th minute in similar circumstances when he converted expertly from Aaron Wan-Bissaka's pass.
Rashford was on hand to lay on the third as Martial completed his hat trick with another well-taken close-range finish. His 14th Premier League goal of the season and 19th in all competitions.
Soon after, United coach Ole Gunnar Solskjaer made five substitutions in one go, introducing Odion Ighalo, Daniel James, Scott McTominay, Juan Mata and Andreas Pereira with Paul Pogba, Mason Greenwood, Bruno Fernandes, Rashford and Martial making way.
"I feel very good, it's the first hat trick in my career," Martial told Manchester United television.
"I'm happy because the team played very good today. [Marcus Rashford] gave me one or two assists today, so the most important thing is to win. I tried to give him a chance to score, no competition, we just want to win."
The hosts missed several chances to add to their tally as Ighalo was denied by Moore and the lively Wan-Bissaka dragged his shot from 10 metres wide of the far post.
Sheffield United, in their third game back, are yet to score a goal since the Premier League's return and have only taken one point from a potential nine available.