Martial started up front with Zlatan Ibrahimovic ruled out for the rest of the season due to a serious knee injury, and Jose Mourinho's decision to attack Burnley with the Frenchman's pace reaped dividends.
United broke off of a Burnley corner after 21 minutes, and Ander Herrera teed up Martial to finish past Tom Heaton from close range.
The Red Devils were two goals up six minutes from the interval as Paul Pogba stole possession and teed up Martial, with Heaton's save falling to captain Rooney to scuff home inside the six-yard box.
The win puts United just a point behind Pep Guardiola's Manchester City before Thursday night's derby clash at the Etihad Stadium, which could well prove to be a top-four shootout.
More to follow.