Leeds United 1 Barnsley 0: Whites on brink of Premier League after surviving major Tykes scare
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Barnsley squandered a fantastic opportunity to take a 27th-minute lead when Mads Andersen put a free header wide from a corner and within 40 seconds United were in front when Michael Sollbauer turned a Patrick Bamford cross into his own net.
It was to prove the only goal of the game as Championship front-runners Leeds again kicked six points clear of third-placed Brentford and five points ahead of second-placed West Brom with just two games left.
Brentford have a far superior goal difference but one more point from United's last two games would guarantee a top-two finish and Leeds will be promoted on Friday evening if West Brom fail to win at Huddersfield Town or on Saturday lunch-time if Brentford are not victorious at Stoke City.
After a quiet opening, Barnsley were handed a glorious chance to strike first in the 11th minute when Jacob Brown was played in behind the Whites defence only to fire his effort across goal without troubling Illan Meslier.
United gradually got going with a Mateusz Klich cross flying through the area before Helder Costa later played a lovely one two with Klich only for his weak shot to hit Bamford who was offside.
But back came Barnsley with a fierce shot from Callum Styles blocked and going for a corner from which Andersen missed a sitter when putting a diving header wide from six yards out and central.
And Andersen's failure to convert was to prove extremely costly with United immediately back on the attack and ultimately taking a 28th minute as Bamford's low cross following a Klich through ball was turned home by Sollbauer for an own goal.
Bielsa then switched Leeds to a 4-4-2 and United squandered a good opening when Costa was unable to find Bamford with his cross after wriggling free on the right.
And United went close to bagging a second in first-half stoppage time when fine skill from Ben White created an attack from which Klich released Harrison whose low cross flew across the area looking for Costa.
Whites head coach Bielsa made a change during the half-time break with Pablo Hernandez replacing Roberts but it was Barnsley substitute Luke Thomas who threatened shortly after the restart when his low shot from the edge of the box forced a solid save from Meslier.
United then lost to Costa to injury with the winger stretchered off as Gjanni Alioski was called for but Barnsley continued to attack and Woodrow miscued a volley well wide before Chaplin flashed a fine effort across goal and inches wide of the post.
After Ayling was dispossessed, Styles then squandered a brilliant chance when firing his effort the wrong side of the post with Chaplin free in an even better position.
The Tykes were causing all sorts of problems and Bielsa reacted by taking off Harrison for defender Pascal Struijk who was moved into centre midfield.
The Reds onslaught continued and Sollbauer's header from an Alex Mowatt free-kick was well saved by Mesler.
United then should have put Barnsley away when Alioski's cross picked out Bamford whose effort was diverted wide by 'keeper Jack Walton.
But Barnsley were largely camped around United's box and only a superb tackle from skipper Liam Cooper stopped Woodrow converting from a corner.
Moments later, Meslier produced a smart save to tip a rising effort from Woodrow over before White diverted a cross wide under pressure from Woodrow.
United were only threatening on the counter and were often guilty of players straying offside during opportunities to break.
Leeds should have had a free-kick on the edge of the box in the 90th minute when Sollbauer hacked down Bamford but the foul went unpunished.
Back came Barnsley but Stuart Dallas was then denied by a flying save from Walton from another Leeds counter as part of a frantic conclusion.
Yet crucially United saw out four minutes of added time and Leeds will now be promoted if taking a point from either Sunday's clash at Derby County or Wednesday night's hosting of Charlton Athletic, if not before should West Brom or Brentford drop points.
Leeds United: Meslier, Ayling, Berardi, Cooper, Dallas, White, Klich, Harrison (Struijk 61), Costa (Alioski 49), Roberts (Hernandez 46, Shackleton 90), Bamford. Subs not used: Casilla, Casey, Douglas, Stevens, Poveda
Barnsley: Walton, J Williams (Oduor 84), Andersen, Brown (Schmidt 78), Woodrow, Chaplin, Ludewig, Sollbauer, Styles, Halme (Thomas 46), Mowatt. Subs not used: Collins, B Williams, Bähre, Ritzmaier, Wolfe, Marsh.
Referee: Jarred Gillett.