The visitors took the lead in the fourth minute of a frenetic first half as they capitalised on a mix-up between Joe Gomez and Alisson Becker, with Rodrigo tapping in, before Mohamed Salah’s 14th-minute finish drew things level again.
Brenden Aaronson almost put Leeds back in front soon after, volleying against the bar, and they subsequently looked set to secure a point after Illan Meslier made a number of fine saves in the second half.
Crysencio Summerville then struck an 89th-minute winner to give the Yorkshire outfit their first victory in nine Premier League games, ending a four-match losing streak, as they moved out of the relegation zone, up to 15th place.
Marsch said: “We talked that last week when it was close with Fulham (a 3-2 home loss) that we were more waiting to lose than pushing to win, and I think the best part was that you saw real resolve at 1-1.
“We needed Illan to make some big saves, but I think the mentality to push, to stay in the match and to see if we could find a way to, regardless, walk away with one (point), (or) get three, was really strong and showed resolve and belief in the team.
“It was necessary to stop the bleeding, really important for us, and I’m happy for our guys.
“We have to use this to launch ourselves. It makes for me next weekend (when Leeds host Bournemouth) really important back at Elland Road.
“I think we should have never been in this situation, because I think we’ve been playing well and just not getting points. But, whatever, we’ve tried to maximise it, stay strong, stay calm and keep pushing.”
Meslier makes it into the latest Premier League team of the week, based on WhoScored ratings, while there is three selections each for Manchester United and Newcastle United while Everton, Arsenal and Man City stars make up the XI. Take a look...
1. Illan Meslier - 9
Made a nine saves against Liverpool with some great goalkeeping. HIs contributions proved invaluable as the Whites claimed a dramatic winner at Anfield to end their eight-game winless run. Photo: OLI SCARFF
2. Diogo Dalot - 8
The right-back's defensive contribution proved vital as Man United recorded a 1-0 win over West Ham. He made four tackles, three interceptions and five clearances as the Red Devils went fifth in the table. Photo: OLI SCARFF
3. Harry Maguire - 8
Back in the side for the first time since Man United's 3-1 win over Arsenal on September 4, Maguire made three blocks and provided eight clearances to help his side edge past West Ham. Photo: Michael Regan
4. Lisandro Martinez - 7.5
A solid display alongside Maguire in the heart of the Man United defence against West Ham. Made two tackles, four blocks and three clearances to help Erik ten Hag's side keep a clean sheet. Photo: Michael Regan