Marsch was fighting for his job as Leeds came into the game lodged in the relegation zone, and the American’s hopes of survival took a turn for the worse when Liam Cooper headed a long ball past his own goalkeeper in the first minute.
Mohamed Salah’s attempt at opening the gift-wrapped opener was denied by a tight angle and recovering defenders before Leeds were handed a present of their own.
Joe Gomez played a backpass across his own goal face without realising Alisson Becker had come wide of his line, leaving Rodrigo Moreno free to tap home a fourth-minute opener.
Anfield was shocked into silence, the atmosphere more reminiscent of a Sunday midday kick-off than a fervent Saturday night under the lights.
They were rescued in typical fashion as Andrew Robertson maintained a bombardment of the Leeds box after a corner was recycled, the ball slotted home by Salah for his 11th goal of the season - only four of which have come in the Premier League.
Liverpool failed to kick on from there and Brenden Aaronson slammed a shot against the crossbar from Rasmus Kristensen’s fine cross from the right.
Darwin Nunez was unable to get the ball out of his feet when sent through one on one as the Reds struggled to dominate their opponents, their next closest effort coming when Robertson tickled the far post with a deflected cross before the break.
Klopp’s troops came out for the second half hardly rallied, allowing Leeds a whiff of a major three points in an increasingly scrappy encounter.
Losing the midfield battle, the Liverpool boss threw on Curtis Jones and Jordan Henderson on the hour mark.
Once again, it was an error that generated their best chance from open play as Cooper got into a muddle with Salah for company, the ball slid in to Nunez whose effort was well blocked by Meslier.
Any momentum fizzled quickly as diving Leeds legs cut off Salah’s next sight of goal before the Egyptian bafflingly toe-poked a good opening into touch - the sort of moment he probably would have scored a goal of the season contender from 18 months ago.
Patrick Bamford is a man certainly out of form and his wayward attempt at controlling a perfect ball into the box squandered Leeds’ best opening after Meslier had again denied Nunez.
The Frenchman was there again to deny Firmino’s late header before Leeds snatched the points through Summerville, the home defence at a standstill as the young winger picked up Bamford’s touch and rolled a shot past Alisson to send the away end wild - and push his team out of the bottom three.