Slaven Bilic's side travelled to Yorkshire knowing they would make history if they avoided defeat at Elland Road.
Never before have an Albion side managed to remain unbeaten in their opening 10 league matches.
They went nine games without a loss at the start of the 1953/54 season as well as the 1999/00 campaign.
And Bilic's men also followed that path with a deflected Ezgjan Alioski strike enough to earn the points for Marcelo Bielsa's side.
In what was a thrilling game throughout, the Baggies arguably should have gone on to claim a point after dominating possession in the second-half.
But while Matheus Pereiera and Grady Diangana consistently combined well, they were unable to create that one clear chance Albion needed to grab a point.
The result means the Baggies drop to second in the Championship, with Leeds replacing them at the top of the table.
Bilic made one change from the team that was so impressive at QPR when naming his starting line-up.
Up front, Hal Robson-Kanu came into the side as the central striker with Charlie Austin forced to make do with a place on the bench.
Otherwise, Albion continued in their 4-2-3-1 system with Matt Phillips on the right-wing, Grady Diangana on the left and Matheus Pereira in the number 10 role.
Notoriously fluid under Bielsa, Leeds effectively began the match in a 4-1-4-1 formation.
It saw Patrick Bamford operate as the centre forward, with Kalvin Phillips the deep-lying midfielder and Helder Costa and Jack Harrison were out wide.
In what proved a breathtaking opening 20 minutes, it was the hosts who started the game on the front.
And they almost broke the deadlock early on in a move that started with a brilliant crossfield pass from Alioski.
That allowed Harrison to find Mateusz Klich in the box who stabbed the ball towards goal.
But Johnstone did well to tip the effort around the post.
Leeds, fresh from losing at Charlton on Saturday, were eager to take the game to Albion with Bilic's side coming under heavy pressure in the opening stages.
Both teams, though, were looking at their most dangerous on the break.
And a frantic 30 second spell saw each side come close to opening the scoring.
It was Leeds who threatened first with Stuart Dallas seeing a shot from the edge of the box blocked by Kyle Bartley.
Albion then raced up the other end through Pereira and Diangana in a move that ended with Robson-Kanu's low drive being saved by Kiko Casilla.
Bilic's side looked more settled as the half-hour mark approached albeit in a match that was both incredibly open and fiery.
For the Baggies, Romaine Sawyers, Bartley and Robson-Kanu all entered the referee's notebook in quick succession.
But in the 38th minute, the hosts got themselves in front through yet another counter-attack.
Harrison twisted and turned his way into the box with it looking at one stage as though Albion had stood up to the threat.
But the Man City loanne managed to the work the ball back to Alioski who saw a low drive deflect off Bartley and fly into the net.
Bilic's side looked to respond immediately with Pereira doing wonderfully well to dance all the way to the byline before being crowded out.
But in the first-half stoppage-time, Albion had Johnstone to thank for only being one down with the keeper making a truly outstanding double save.
After Alioski tried his luck from distance, Bamford prodded the ball towards goal from close range.
But not only did Johnstone get down to parry that away, he then raced back up to his feet to spectacularly prevent Costa from nodding in.
Perhaps buoyed by that Johnstone, save, Albion started brightly following the interval.
Diangana did well to win the ball on half-way before sending Pereira charging into the box.
But from a tight-angle, the Brazilian then flashes a strike right across the face of goal.
Then just a few moments later, the Sportling loanee again went close with Pereira sending a free-kick from 25-yards just millimetres past the post.
Bilic made a double change on the hour with Filip Krovinovic and Kenneth Zohore replacing Phillips and Robson-Kanu.
It was Leeds though who threatened next with Johnstone beating away an effort from Costa with Bartley then making a good block to deny Klich.
Albion, though, hit-back with Diangana sending in a cross which Pereira turned goalwards only for Casilla to get down and parry the ball away.
As the clock ticked past the 70-minute mark, the game again became incredibly open.
It was the Baggies, though, who were now dominating the ball with Pereira, Krovinovic and Diangana all combing well.
But for all their good play they just couldn't find that killer pass or finish.
And that meant it was Leeds who were able to dig in and claim the win.
Leeds: Casilla, Alioski, White, Cooper (Berardi 34), Dallas, Phillips, Shackleton (Roberts 45, Ayling 75), Klich, Costa, Harrison, Bamford.
Subs not used: Maizek, Douglas, Clarke, Nketiah.
Albion (4-2-3-1): Johnstone, Furlong, Ajayi, Bartley, Ferguson, Livermore (Edwards 82), Sawyers, Phillips (Krovinovic 62), Pereira, Diangana, Robson-Kanu (Zohore 62).
Subs not used: Bond, O'Shea, Townsend, Austin.