Rashford scored one goal and was behind most of United’s best moves as the home team continued their recent revival under Ole Gunnar Solskjaer.
After Paul Pogba had curled an effort wide and Victor Lindelof headed Ashley Young’s cross off target, United went close to taking the lead in the 20th minute when Shane Duffy headed Rashford’s shot off the line.
Pogba’s overhead kick flew wide and Rashford bent a shot over the bar before Solskjaer’s team were awarded a penalty in the 27th minute when Gaetan Bong bundled Pogba over. The France international got up to slot his spot-kick past David Button in the Seagulls' goal.
United went close to doubling their advantage nine minutes later when Button denied Anthony Martial while at the other end veteran striker Glenn Murray blasted a half-volley wide.
United made it 2-0 three minutes before the interval when Rashford beat Pascal Gross before firing into the top corner of Button’s net.
The home team continued to be the better side in the second period and Martial almost got on the scoresheet in the 57th minute, only to drag his shot narrowly wide before Pogba blasted a shot over the bar.
However, Chris Hughton’s team halved the deficit with 18 minutes left when Gross controlled Davy Propper’s ball forward before firing his shot past David de Gea and in off the crossbar.
The goal lifted Brighton and United had to endure a few nervy moments in the closing stages before eventually being able to celebrate another three points.