In the first league meeting between these teams in 16 years, five goals were scored in an exhilarating first half, with McTominay becoming the first player in Premier League history to score twice inside three minutes.
Bruno Fernandes and Victor Lindelof were also on target for the hosts, who went 4-0 up before Liam Cooper headed home for Leeds shortly before half-time.
Daniel James and Fernandes scored second-half goals for Manchester United, who blew Leeds away despite Stuart Dallas netting a superb consolation goal.
Old rivals Manchester United and Leeds United were meeting in the league for the first time since 2004 and the clash did not disappoint.
It took Ole Gunnar Solskjaer’s side just 67 seconds to take the lead as United stole possession and McTominay rifled home from the edge of the box.
The Scotland international scored again less than two minutes later, making the most of Anthony Martial’s superb through ball to beat Leeds goalkeeper Illan Meslier.
While Leeds began to threaten, the hosts continued to be clinical in front of goal and in-form Fernandes drilled home their third after 20 minutes.
Leeds, who won the Championship last season, would have been fearing the worst when Lindelof scored United’s fourth, but they at least went in at the break with a goal thanks to Cooper’s header.
Marco Bielsa’s side continued to create chances after the interval – Raphinha was denied twice by David de Gea – but Manchester United were clinical in the final third and James made the most of his rare start when he added a fifth.
Solskjaer’s side were awarded a penalty shortly after when Martial was tripped by Pascal Struijk, and Fernandes made no mistake from the spot to put his team 6-1 ahead.
An incredibly open game continued to produce chances and Leeds’ Dallas scored one of the best goals of the match when he bent a long-range effort past the out-stretched De Gea.
Manchester United came close to extending their lead even further through Fred and second-half substitutes Edinson Cavani and Alex Telles, but a brilliant Premier League fixture ended 6-2.
The victory sees Solskjaer’s side move to third in the Premier League – five points behind reigning champions Liverpool – while Leeds stay 14th.