Man United left it late to secure the three points at Elland Road as Rashford and Alejandro Garnacho each scored in the space of five blistering minutes.
The visitors opened the scoring when Luke Shaw expertly picked out Rashford, who completed the move with a wonderful headed goal.
The 25-year-old brought up his 12th league goal of the season as he enjoys a superb spell following the 2022 World Cup, where he starred for England.
Erik ten Hag’s side then made it 2-0 in the 85th after second-half substitute Garnacho found the back of the net with a tidy finish.
Wout Weghorst slid a ball into the Argentine winger, who showed off his pace to beat his marker before scoring past Illan Meslier.
Rashford’s goal was the talk of social media as Man United fans praised his goal against Leeds.
Rio Ferdinand tweeted: “Shaw to Rashford… some form right now!!”
A second wrote: “Marcus Rashford superb finish after a perfectly placed cross from Luke Shaw. He’s him!”
A third added: “A moment of sheer quality. Sabitzer to Shaw to Rashford. It’s a wonderful goal, it’s a wonderful header.”
A fourth commented: “Rashford is too good now!”
Another boldly claimed: “Best player in the world rn.”
Man United, who drew 2-2 with Leeds earlier in the week, move above Manchester City to second in the league, five points adrift of league leaders Arsenal.