Despite a lively start from the visitors, Leeds struck first through Raphinha, and the hosts were good value for their lead in the first half.
However, they were unable to withstand the West Ham fightback after the break, fatigue beginning to show as a Junior Firpo own-goal made it 1-1 before Antonio snatched the victory late on.
Story of the match
Leeds' side was depleted due to injuries, with regular starters Patrick Bamford and Luke Ayling both missing. Further absentees in the defensive department also meant there was a Premier League debut for 18-year-old centre back, Charlie Cresswell.
The French goalkeeper was forced into another fine stop soon after, Benrahma trying his luck again with a curler from just outside the box, but his shot was tipped wide for a corner.
Leeds managed to launch a counter attack from the resulting set piece as the frantic tempo continued, and Benhrama was involved again, this time making a vital last-ditch interception to prevent Rodrigo from racing in behind.
Just before the 15-minute mark it was Lukasz Fabianski's turn to produce a spectacular stop, and he pushed Stuart Dallas' strike over the bar. Both 'keepers busy as the two sides continued to threaten.
The deadlock was eventually broken on 19 minutes when the hosts capitalised on Tomas Soucek's underhit ball, making two quick passes forwards before Raphinha found space and then the far corner to make it 1-0 Leeds.
Elland Road was rocking after the opener, and the energy was feeding onto the pitch with the pace of the game remaining fast even if there were fewer clear cut chances in the period that followed the goal.
The next significant attempt was a carbon copy of the effort that put Leeds ahead, Raphinha's left foot aiming to find the same corner, however this time the post came to West Ham's rescue, and the ball bounced away from danger.
Marcelo Bielsa's team controlled the game after taking the lead, keeping possession well and showing the better energy levels as they were first to every loose ball. While the early stages belonged to West Ham, the home team were dominant for the rest of the first half.
A golden opportunity was presented for the visitors to equalise just before the interval when Pablo Fornals raced on to Antonio's incisive through ball, however the Spaniard could not convert the one-on-one.
Meslier held his position well to close the angle, and made yet another great save to keep his team in front heading into the break.
Leeds United (@LUFC) September 25, 2021
Tomas Soucek, who had a poor first-half, thought he'd equalised for the Hammers on 52 minutes when he poked home following a free-kick, however a VAR check ruled out the goal due to a foul by Antonio on Meslier in the build-up.
West Ham showed some improvement after the disallowed goal, building momentum with a couple of corners, although Meslier continued his fine afternoon, keeping out Soucek's header and everything else thrown at him.
Despite the Hammers creating more, Klich should have doubled his team's advantage, but the midfielder failed to hit the target after a cutback from Raphinha, the Brazilian winger continuing to cause problems down the right.
The midfielder was left to rue his missed chance as West Ham equalised moments later on 70 minutes, Jarrod Bowen cutting in from the right and eventually finding the back of the net thanks to a double deflection. A deserved goal for both the player and his team to make it 1-1.
David Moyes' men grew in confidence after drawing level, beginning to set the tempo of the fixture with much quicker passing than before the break.
Spaces began to open up in behind the Leeds defence and Antonio looked to take advantage, a last-ditch block from skipper Liam Cooper preventing the number 9 from scoring.
Heading into the final 10 the home team began to tire, West Ham looking the more likely team to grab a late winner as they threw men forwards in search of three points.
Moyes' men did exactly that in the 90th minute.
Declan Rice surged forwards before picking out Antonio, and then the forward did the rest, showing awareness to glide by Shackleton and composure to slot it past Meslier. A true striker's finish.
Kalvin Phillips hit one wide from distance in an attempt to salvage a point in injury time, and the Hammers held on for victory.
Leeds, who were without several key players, remain winless in the Premier League this season, while the Hammers continue their impressive start to the campaign, rising to seventh.