Parker’s men were good value for their 2-0 victory, although it required two goals of real quality to take the win.
While Leeds dominated much of the possession, their only chances of the game came from Burnley mistakes - and the home side otherwise looked relatively comfortable keeping them at bay.
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There was an anxious spell midway through the second-half as Leeds came on strong, but Tchaouna relieved that pressure with a superb second from long range.
Burnley now move up to 17th, two points ahead of Nottingham Forest who dispensed with the services of Ange Postecoglou after just 39 days following their 3-0 defeat to Chelsea.
Here’s how Burnley’s players rated:
Turned up in the big moments to make some crucial saves, none more so than in the first-half when he turned Aaronson’s shot onto the post (Photo by ANDY BUCHANAN/AFP via Getty Images)
1. Martin Dubravka - 8/10
Turned up in the big moments to make some crucial saves, none more so than in the first-half when he turned Aaronson’s shot onto the post (Photo by ANDY BUCHANAN/AFP via Getty Images) Photo: ANDY BUCHANAN
Involved in both goals, providing the pinpoint cross for Ugochukwu’s header before getting Burnley 60 yards up the pitch before the second. Photo: Kelvin Lister-Stuttard
2. Kyle Walker - 8/10
Involved in both goals, providing the pinpoint cross for Ugochukwu’s header before getting Burnley 60 yards up the pitch before the second. Photo: Kelvin Lister-Stuttard Photo: Kelvin Lister-Stuttard
Much steadier than he was at Villa Park prior to the break. Blocked everything and produced a vital clearance after Burnley had given the ball away. (Photo by ANDY BUCHANAN/AFP via Getty Images)
3. Axel Tuanzebe - 7/10
Much steadier than he was at Villa Park prior to the break. Blocked everything and produced a vital clearance after Burnley had given the ball away. (Photo by ANDY BUCHANAN/AFP via Getty Images) Photo: ANDY BUCHANAN
Looks at home in a back four, much more settled. Swept up any danger without any fuss (Photo by ANDY BUCHANAN/AFP via Getty Images)
4. Maxime Esteve - 7/10
Looks at home in a back four, much more settled. Swept up any danger without any fuss (Photo by ANDY BUCHANAN/AFP via Getty Images) Photo: ANDY BUCHANAN