“A win today would take the pressure off”, the Whites legend correctly opined.
In the event, Leeds suffered a punishing late defeat, made all the more sore by the fact that looked like their old selves, in terms of their effervescent attacking work for much of the game.
Granted, they were indebted to some quality goalkeeping for spells from Illan Meslier, but their performance in the other direction was eye-catching.
Unfortunately, games are often decided in quick-fire pockets of play and this was the case here.
Leading 1-0, thanks to an excellent 19th-minute strike from the irrepressible Raphinha, Mateusz Klich had a golden spell to double the advantage on 64 minutes when played in by the gifted Brazilian.
Instead of scoring, he missed and the game switched.
Three minutes later, a shot from Jarrod Bowen hit impressive debutant Charlie Cresswell and then truly take a wicked second deflection off Junior Firpo to finally beat Meslier and that was an the incentive that the Hammers had to push for the winner.
It arrived late on when Michal Antonio - who had earlier seen a goal ruled out for a clear foul on Meslier, who needed treatment after being caught by his flailing arm - skipped past Jamie Shackleton and broke Leeds hearts after latching onto Declan Rice's pass.
It was cruel on Leeds, who have now equaled their worst-ever start to a league season.
Ahead of the game, much had been made of the battle in midfield between England internationals Kalvin Phillips and Rice, but in the event, they did not cover themselves in glory in the first half with the bouquets reserved for others. Unfortunately, Rice did conjure one big moment when it mattered.
Said Benrahma, so often a thorn for Leeds, posed his traditional problems, but fortunately at the other end, the hosts had several players in the mood, most notably Raphinha and Rodrigo.
They also had a goalkeeper in tip-top form in Meslier and it was just as well.
The Frenchman first stepped up the plate to get a key touch to a fierce angled shot from Michail Antonio, available again after suspension and then made a fine one-handed save to divert Benrahma’s curler as the Hammers were afforded joy in the opening ten minutes.
Just before the break, Meslier again showed his mettle, making a hugely important one-on-one save to thwart Pablo Fornals, who surged clear after Phillips misjudged a throughball.
Despite a testing start, there was plenty to admire about Leeds, who handed a league debut to Charlie Cresswell, who did not look overawed whatsoever, with one cool side-step of West Ham defender Angelo Ogbonna when in possession early on confirming that.
Their offensive play was fluid and eye-catching, in keeping with their beguiling return to the Premier League last term and their opener was a beauty.
Tomas Soucek underhit a pass and Leeds were on it in an instant with Rodrigo - whose movement posed major issues for West Ham - powering forward before picking out Mateusz Klich, who had the vision to notice the untracked Raphinha.
He found the Brazilian and his low finish was deadly and a gem.
Soon after, Raphinha almost provided an encore with his precision low shot striking the post with the Hammers struggling to deal with him.
Stuart Dallas had earlier gone close when his shot was tipped over by Fabianski, while the number of chances that West Ham - unbeaten in the league on their travels since April - created at the other end was more than enough to keep them interested.
Antonio stuck out a leg at the back post and almost diverted a cross-shot from Benrahma into the net and after Meslier’s key save to thwart Fornals, Jarrod Bowen cut inside and was a whisker away from levelling with a curler which flew inches wide ahead of half-time.
James made way at the break for Harrison with Leeds going close to a second early on the restart with Ogbonna bundling the ball just wide of his own goal under pressure from Cresswell following a corner from Dallas.
Soon after, Kurt Zouma made a key block to get in the way of Harrison’s goalbound drive after Raphinha and Rodrigo again undressed West Ham.
At the other end, the Hammers then celebrated what they thought was a leveller after Soucek converted the loose ball, but VAR correctly ruled it out for Antonio’s clear foul on Meslier in the build-up.
It was certainly an eventiful afternoon for Meslier, who then made another smart stop to claw out a header from Soucek, who had risen above Liam Cooper following a Hammers corner.
Soon after, Leeds spurned a golden chance to perhaps make the game safe after more sublime play from Raphinha.
He picked out Klich following a searing break down the right, but the Pole’s aim was wayward and he fired the ball wastefully wide with plenty of the goal to aim at and West Ham breathed a sign of relief.
The gravity of that miss was soon exposed when West Ham, albeit in fortuitous fashion courtesy of a deflected effort from Bowen, given too much space down the right after cutting inside.
The narrative of the game switched and Leeds were now facing a test of character, with Antonio soon firing over after the loose ball fell to him after Meslier failed to gather amid a sea of bodies in the Leeds box.
West Ham now had the whiff of victory in their nostrils, with Cresswell continuing his sound league debut to get in the way of a drive from Antonio after the powerful Hammers forward had cut inside.
But he could do nothing about Antonio's winner, with Leeds now facing a huge game at home to Watford next weekend.
Leeds United: Meslier; Shackleton (Summerville 90), C Cresswell, Cooper, Firpo; Phillips, Dallas; Raphinha (Roberts 69), Klich, James (Harrison 45); Rodrigo. Substitutes unused: Klaesson, Gelhardt, Hjelde, Drameh, Greenwood, McCarron.
West Ham: Fabianski; Coufal, Zouma, Ogbonna, A Cresswell; Soucek, Rice; Bowen (Dawson 90), Fornals (Vlasic 78), Benrahma; Antonio (Yarmolenko 90). Substitutes unused: Areola, Lanzini, Noble, Diop, Johnson, Kral.
Referee: K Friend (Leicestershire).