United manager Jose Mourinho says he “let the horses run freely”.
Eric Bailly, Paul Pogba and substitute Anthony Martial also found the net at the Liberty Stadium, giving Jose Mourinho's side their second big win after last weekend's 4-0 victory over West Ham United.
Sadio Mane struck in the 73rd minute to give Liverpool a 1-0 home win over Crystal Palace and get Jurgen Klopp's side up and running after their 3-3 draw at Watford on the opening weekend.
"The team was confident from the first minute," said Mourinho after a result that means United have scored four goals in their first two league games for the first time in 110 years.
"I like to see the confidence that the players are having in this moment. There's no panic. The team was always confident and always trying to move the ball. I'm really happy."
Having had to work hard to break Swansea down, United went in front just before half-time when Bailly stabbed in his first goal for the club after Lukasz Fabianski had pushed Pogba's header against the bar.
Attacking changes left Swansea vulnerable at the back in the latter stages and United took full advantage to score three goals in the space of just four minutes.
In the 80th minute Henrikh Mkhitaryan teed up Lukaku for his fourth goal in three United games since signing from Everton.
Mkhitaryan then freed Pogba to beat Fabianski with a delightful dinked finish before Martial tucked in a fourth.