The Frenchman scored twice in the first half and again after the break to stretch United's unbeaten run to 13 games and leave them just two points behind Chelsea, who play Manchester City at Stamford Bridge on Thursday. Martial's hat trick, capped with a wonderful third at the end of a move that involved Paul Pogba, Bruno Fernandes and Marcus Rashford, was his first in senior football and United's first in the league since Robin van Persie's against Aston Villa in April 2013 when Sir Alex Ferguson was still in charge.
Solskjaer put a lot of faith in Martial when Romelu Lukaku left, making the 24-year-old his first-choice centre-forward after he had spent most of his United career on the wing. He has had poor games -- Tottenham on Friday was one -- but his three goals against Sheffield United took him to 19 for the season, his best tally since arriving at Old Trafford in 2015.
There wasn't much wrong with the performance, but Rashford will be disappointed he didn't take two good chances in the first half. It's perhaps to be expected after being sidelined since January and training at home for three months. Solskjaer will hope his sharpness in front of goal returns soon.
Manager rating out of 10
8 -- The Norwegian picked an attacking team with Fernandes, Pogba, Rashford, Martial and Mason Greenwood in the same XI for the first time, and it paid off. United were 2-0 up at half-time but it could have been five had they taken their chances.
Player ratings (1-10; 10 = best. Players introduced after 70 minutes get no rating)
GK David De Gea, 7 -- Had very little to do. The perfect game with the spotlight on him after his mistake at Tottenham.
MF Nemanja Matic, 7 -- Provided valuable insurance in midfield with Pogba and Fernandes always looking to go forward.
MF Paul Pogba, 7 -- Making his first start since September, he delivered one lovely dinked pass over the top for Rashford and played his part in Martial's third.
MF Bruno Fernandes, 8 -- Tested Simon Moore with a fierce free kick from a tight angle on the left. Always busy and inventive.
FW Mason Greenwood, 7 -- Replaced Daniel James in the starting XI and might have scored had Pogba not deflected his low shot wide early in the second half.
FW Marcus Rashford, 7 -- Made a clever touch and cross to give Martial the chance to open the scoring after six minutes but missed two golden chances.
FW Anthony Martial, 9 -- First two goals were instinctive finishes and the third was a wonderful clipped effort to round off a terrific team move and wrap up his first senior hat trick.
FW Odion Ighalo, N/R -- Had one chance to add to his United goal tally but a missed touch cost him.
FW Daniel James, N/R -- On for Greenwood as United strolled to the finish line.
MF Juan Mata, N/R -- Replaced Rashford and nearly grabbed an assist in the final moments.
MF Scott McTominay, N/R -- Fresh off his new contract, McTominay wasn't asked to do much here.
MF Andreas Pereira, N/R -- Replaced Fernandes on 79 minutes as part of Solskjaer's full five-man substitution.