The Whites were beaten 1-0 thanks to a second half goal from Harvey Barnes, but they created a host of chances themselves that they just couldn't convert.
Raphinha came closest with an opportunity from a couple of yards out that Kasper Schmeichel somehow kept out.
Marsch was handed more misfortune late in the game as his final substitute, Tyler Roberts, suffered an injury and was essentially a spectator as he limped around the pitch.
Leeds could be caught by Burnley, who currently head the three teams in the drop zone, this evening if the Clarets manage to pull off a shock win over Chelsea. Everton, the side directly below the Whites, visit Spurs on Monday night.
1. Illan Meslier - 7
Cool under pressure with the ball at his feet, made a couple of saves, got a fingertip to a great finish for the winner
2. Luke Ayling - 8
Defended well, got on the ball to good effect and pushed Leeds forward. Clever and gritty performance
3. Junior Firpo - 7
Did both sides of the game well. Got up and down the flank all afternoon, contributing to the attack. Unlucky not to score
4. Robin Koch - 6
Got stuck in, tried to contribute on the ball but at times lacked composure in possession
5. Pascal Struijk - 7
Largely solid. Vardy got the better of him that led to a yellow card but Struijk gave him little else
6. Stuart Dallas - 7
Ran himself into the ground.Under pressure early on defensively but grew into the game and performed well.