Putting aside the spectre of Manchester City winning the title in next weekend’s derby, Jose Mourinho’s men regained second spot from Liverpool thanks to a superb first-half display.
Lukaku’s 100th top-flight goal was complemented by Alexis Sanchez’s second since arriving in January as United ran out deserved 2-0 victors at home to Swansea.
Earlier,Liverpool had kept up the pressure on United as they came from behind to win 2-1 at Crystal Palace with a late goal by Mohamed Salah.
Jermain Defoe came off the bench to net a stoppage-time equaliser as Bournemouth snatched a 2-2 draw at Watford.
Bottom club West Brom edged another step closer to relegation by losing 2-1 at home to Burnley.
Newcastle boosted their own survival hopes and dented Huddersfield’s with a 1-0 win at St James’ Park.
Ayoze Perez struck with only ten minutes left to push the Toon Army up to 12th place and leave the Terriers only three points above the drop zone.
Leicester scored two late goals to beat Brighton 2-0 at the King Power Stadium, where they finished with ten men.
The Seagulls had just seen Glenn Murray’s penalty saved before Vicente Iborra broke the deadlock on 83 minutes.
Leicester midfielder Wilfred Ndidi was sent off for a second caution with three minutes left but Jamie Vardy slotted in during added time.