United's £72m summer signing from Atalanta has hit a red-hot streak after early struggles in front of goal and scored twice in the first seven minutes to set up a fourth successive league win for Erik ten Hag's side.
The 21-year-old pounced on Amari'i Bell's error after only 37 seconds to round keeper Thomas Kaminski and score, adding a second in the seventh minute, instinctively diverting Alejandro Garnacho's shot into the net.
Luton Town, in an uproarious atmosphere, responded with defiance and character, Carlton Morris swiftly giving the Hatters hope with a header as United struggled to cope with the intensity of the home side, especially in the opening half.
United lost defender Luke Shaw to injury before the interval, while Harry Maguire and Casemiro also went off at the break, but for all Luton's second-half endeavour it was the visitors who created the better chances, Kaminski denying Garnacho, Rashford, and a Hojlund hat-trick.
However, there was one more nervous moment for the visitors in stoppage time when Ross Barkley's glancing header clipped the top of the crossbar.
The win means United are now only five points behind fourth-placed Aston Villa.
-- Courtesy of BBC Sport