Wayne Routledge grabbed a 90th minute winner to give Swansea City a first victory at Elland Road in 70 years and extend their unbeaten start to life under Steve Cooper.
Substitute Routledge swept home a deflected Matt Grimes cross via the inside of the post to send the Swans top of the Championship table.
The visitors were under the cosh for long spells of the afternoon but, in truth, keeper Freddie Woodman did not have too many saves to make as those in front of him made block after block and clearance after clearance to ensure a third clean sheet of the season.
Homegrown products Connor Roberts and Joe Rodon were among those to stand out, while the Swans will also have cause to feel they could have made more of a handful of promising attacks, with Bersant Celina and substitute Sam Surridge unable to convert the best of them.
But it did not matter as Routledge converted to give the visitors just their second ever win at the home of the Yorkshire club.
And winning at a ground that has long been a graveyard for Swansea sides down the years is a major statement for Cooper and company heading into the international break.
The head coach had stuck with the same starting XI and bench that had beaten Birmingham
There was an early scare for the Swans as Woodman had to scurry across to prevent Mike van der Hoorn’s block finding its way in at his near post.
The Swans keeper was soon in action again, holding Ezgjan Alioski’s volley from a fine Pablo Hernandez cross.
Leeds were flooding numbers forward at every opportunity and it took some excellent defending from Roberts to keep Stuart Dallas at bay from one particularly rapid counter.
Patrick Bamford wasted the hosts best chance yet in the 16th minute, sending a free header miles wide of the target from a Dallas cross.
The pressure increased, Bamford heading wide again when well placed as the half-hour mark neared.
Swansea had barely threatened, although one wonderful run out of defence by Celina nearly got the Kosovo international in on goal, but Borja’s final pass was just cut out by Ben White’s despairing slide.
Matt Grimes put a free-kick into the side-netting after more neat passing had forced Jack Harrison to fell Roberts on the edge of the box.
Swansea had shown signs of settling, but Leeds served up a reminder of their threat when Liam Cooper crashed a header against the bar in first-half stoppage time.
The home side were on the front foot again shortly after the break, ex-Swan Hernandez getting away a volley that Woodman comfortably held.
There was plenty of endeavour but little goalmouth action during the early stages of the half and both managers made changes.
Bielsa sent on Eddie Nketiah for Bamford, while Sam Surridge and Routledge replaced Borja and Yan Dhanda respectively.
Nketiah fired over under pressure from Roberts as the on loan forward looked to make his presence felt.
Swansea responded with Surridge digging out a cross to the back post, but Celina opted to head across goal for a team-mate when the chance was there to hit the target.
Roberts then made a superb block as Harrison’s eyes lit up when a ball fell to him in the area following a slaloming run from Hernandez.
Woodman lifted the siege with a wonderful long pass for Celina, who drove at the defence and won a corner, which a worried Dallas chested narrowly past his own post.
Leeds were pressing but Swansea were countering effectively. Surridge had penalty appeals waved away as keeper Kiko Casilla attempted to smother the ball at the striker’s feet, before the on-loan Bournemouth man guided a Roberts’ cross over the bar.
However, Leeds did not clear the pressure and Routledge took full advantage on an historic day for the Swans.
Leeds United: Kiko Casilla; Stuart Dallas, Liam Cooper (captain), Ben White, Ezgjan Alioski (Barry Douglas 83); Kalvin Phillips; Pablo Hernandez, Mateusz Klich (Helder Costa 71), Adam Forshaw, Jack Harrison; Patrick Bamford (Eddie Nketiah 61).
Subs not used: Illan Meslier, Gaetano Berardi, Alfie McCalmont, Jamie Shackleton.
Swansea City: Freddie Woodman; Connor Roberts, Mike van der Hoorn, Joe Rodon, Jake Bidwell; Jay Fulton, Matt Grimes (captain); Andre Ayew (George Byers 85), Yan Dhanda (Wayne Routledge 63), Bersant Celina; Borja Baston (Sam Surridge 63).
Subs not used: Kristoffer Nordfeldt, Kyle Naughton, Ben Wilmot, Jordon Garrick.
Referee: Darren Bond
Attendance: 34, 935