Lukaku gave United an early lead when he collected Alexis Sanchez’s pass to fire in with the aid of a deflection.
Sanchez’s crisp strike soon doubled the advantage – only his second league goal for United – as the hosts dominated.
Swansea improved after the break, Tammy Abraham twice denied by David de Gea, but United were always in control.
Jose Mourinho’s side re-opened a two-point gap over third-placed Liverpool, who won 2-1 at Crystal Palace earlier on Saturday.
Swansea stay three points clear of the relegation zone, but drop down a place to 15th.
Belgium striker Lukaku has divided opinion among Manchester United fans at times during his first season following the £75m move from Everton last summer, but again demonstrated his quality with a clinical strike that set them on the way to a comfortable win.
Lukaku took one touch to control Sanchez’s pass, creating space inside the Swansea box to hammer in.
It was richly deserved lead for the home side, who started the game at a high tempo, and one which they never looked like relinquishing.
Lukaku has now scored 26 goals for the club this season, despite suffering some criticism after scoring just once in 12 games in October and November.
The 24-year-old, who has also played for Chelsea, West Brom and Everton, becomes the youngest foreign player to reach a century of Premier League goals.
“I’m really happy to achieve that milestone,” he said.
“It is a dream come true. l’m really happy to achieve that in a league I’ve wanted to play in since I was six years old.”
