Swansea City 0 Leeds United 1: Dramatic Pablo Hernandez winner sees Whites close in on Premier League football
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The contest looked destined to end in a goalless draw but with time running out Luke Ayling started a flowing counter that was finished by Spanish magician Hernandez to send Whites fans into raptures around the globe.
The victory sent Leeds three points clear of second-placed West Brom and re-established a six-point cushion in the division's automatic promotion spots with three games left.
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Hide AdEven if Brentford and West Brom win all of their remaining games, four points from United's final three games at home to Barnsley and Charlton Athletic and away at Derby County will put the Whites in the Premier League.
Leeds began brightly and an early Kalvin Phillips free-kick needed to be scrambled behind for a corner from which Ben Cabango's clearance under pressure from Patrick Bamford flashed just wide.
But the first real chance arrived for Swansea in the ninth minute when Liverpool loanee Rhian Brewster found space in the area and saw his firm low shot well held by 'keeper Illan Meslier.
Luke Ayling then blocked Conor Gallagher's shot which deflected behind for a corner which Leeds survived as part of an open start with United saved by a fantastic sliding clearance from Ayling to prevent a through ball reaching Brewster.
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Hide AdJay Fulton then blasted a shot well over the bar and back came Leeds with Jack Harrison's cross trickling just wide.
United then improved after Whites head coach Marcelo Bielsa's instructions during the drinks break with 'keeper Freddie Woodman tipping away a decent low drive from Stuart Dallas.
Patrick Bamford then looked set to cash in on slack Swans defending but his volley was placed straight at Woodman who saved.
A Swansea free-kick then caused United bother with Andre Ayew beating Meslier to the ball but Ayling making a strong block.
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Hide AdA fine run by Helder Costa then took the winger into the Swansea box but Woodman proved equal to his shot and the half ended with Tyler Roberts looking to play in Bamford but with the Swans defence intercepting.
Bielsa opted to make a double change during the interval with Pablo Hernandez replacing Roberts and Gjanni Alioski coming on for Stuart Dallas.
United began the second half well with a few shots from the edge of the area blocked before two good crosses from Ayling came to nothing.
But only a fine save from Meslier then kept the score goalless with the Leeds 'keeper tipping a ferocious drive from Gallagher over the bar.
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Hide AdYet United squandered their best chance yet in the 64th minute when a fantastic first-time cross from Jack Harrison following a raking Hernandez pass created an opening for Bamford whose diving header from close range was kept out by Woodman.
Ayling then walloped a volley over before United were unable to capitalise on two rapid counters with Costa offside when looking to latch on to a Hernandez pass for the second chance.
Another gem of a pass from Hernandez then set up Harrison who lashed his effort over the bar.
From a fine move, Hernandez then fired a shot from the edge of the area narrowly over.
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Hide AdUnited looked to be running out of time but from a flowing counter attack started by Ayling, magic man Hernandez finally fired Leeds in front with a neat finish that beat Woodman in off the post in the 89th minute.
Leeds United: Meslier, Ayling, White, Cooper, Dallas (Alioski 46), Phillips, Klich, Harrison (Berardi 90), Costa (Shackleton 90), Roberts (Hernandez 46), Bamford. Subs not used: Miazek, Douglas, Bogusz, Poveda, Struijk.
Swansea City: Woodman (Mulder 90); Naughton, Cabango, Guehi (Celina 90); Roberts, Fulton (Byers 90), Grimes, Bidwell (Cullen 90); Gallagher, Ayew; Brewster (Routledge 81). Subs not used: van der Hoorn, Dyer, Kalulu, Dhanda.
Referee: Keith Stroud.