Jurgen Klopp’s side took control thanks to first-half goals from Trent Alexander-Arnold and Mohamed Salah behind closed doors at Anfield.
Fabinho and Sadio Mane netted after the interval and Liverpool will be crowned champions if Manchester City fail to beat Chelsea at Stamford Bridge tonight.
If second-placed City win in west London, then Liverpool could wrap up their first English title for 30 years in their next game - against Pep Guardiola’s side at the Etihad Stadium on July 2.
“Imagine if the stadium could have been full and people could have experienced that live. It would have been amazing,” Klopp said.
“The atmosphere on the pitch was incredible. That was the best counter-pressing game I have ever seen behind closed doors.
“The attitude the boys showed was amazing.”
Asked if he would be watching when City face Chelsea, Klopp added: “Tonight was a big step, that’s clear. I have to watch the game tomorrow because we play them one week later.
“That’s being professional and doing my job.”
After a drab goalless draw at Merseyside rivals Everton on Sunday, the champions-elect were far more vibrant and Alexander-Arnold opened the scoring with a superb free-kick in the 23rd minute.
Salah doubled the lead in the 44th minute, taking Fabinho’s lofted pass and guiding in his 21st goal of the season.
Fabinho scored with a thunderous 30-yard strike in the 55th minute and Mane capped a fine move in the 69th minute as Liverpool moved 23 points clear of City.
United are still far off challenging again for titles at the top of the table, but there are growing signs of momentum for Ole Gunnar Solskjaer’s men as they extended their unbeaten run to 13 games.
Martial produced two predatory first-time finishes before half-time to put United in command at Old Trafford.
Sheffield United were riding high in March before football’s shutdown for three months, but the Blades have now picked up just one point and failed to score in their three games since the restart.
United could have piled on much more pain after the break, but were content with one more goal as Martial completed his first career hat-trick with a cheeky chip from Marcus Rashford’s pass.
“Very happy for Anthony,” Solskjaer said. “The third goal was a great goal, but for me the first and the second were better.
“He’s in the box, ready to go. We have worked on that, getting in the box in that situation more often.
“I thought our performance deserved a win, definitely.”
Fifth-place could still be good enough for a place in next season’s Champions League depending on the outcome of City’s appeal against a two-season ban from European competition.
And Wolves remain level on points with United in fifth after continuing their perfect restart with a 1-0 win over Bournemouth.
Just as in a 2-0 victory at West Ham on Saturday, Adama Traore and Raul Jimenez combined to break the deadlock as the Mexican powered home a header for his 24th goal of the season.
Defeat leaves Bournemouth still in the bottom three on goal difference and there are now three teams tied on 27 points as Aston Villa struck late to claim a 1-1 draw at Newcastle.
Dean Smith’s side looked set to rue a host of missed chances before half-time when Dwight Gayle put the Magpies in front.
However, Ahmed El Mohamady’s scrappy finish from Conor Hourihane’s corner salvaged a precious point.
Any hope of Norwich hauling themselves out of trouble now looks forlorn as the Canaries fell to a second home defeat in a week.
Michael Keane scored the only goal as Everton won 1-0 at Carrow Road to move above Arsenal into 10th.
Norwich remain rock bottom, six points adrift of safety.