Scott Parker’s side showed plenty of character to stay in the game during the second-half after suffering a nightmare end to the first 45 minutes.
Despite playing well for the first half an hour, Burnley suffered a soft first goal from a direct corner before being reduced to 10 men through Lucas Pires' straight red.
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An Anthony Gordon penalty in first-half stoppage-time looked to set up a miserable second period, but the Clarets reduced the deficit through Zian Flemming before glancing a header agonisingly wide of the far post with the last action of the game.
Here’s how Burnley’s players rated:
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9. Lyle Foster - 6/10
Did okay out on the right, threatening with an early header and curling just wide. Taken off at half-time as Burnley added an extra defender following the red. Photo: Kelvin Lister-Stuttard Photo: Kelvin Lister-Stuttard
10. Jacob Bruun Larsen - 7/10
Back in the starting XI in his favoured left wing role and started well, before putting in a big defensive shift after the red card. Photo: Kelvin Lister-Stuttard Photo: Kelvin Lister-Stuttard
11. Armando Broja - 7/10
Did well on his first league start for Burnley, battling and competing for everything. Had an early chance of sorts when his block ricocheted towards goal. Photo: Kelvin Lister-Stuttard Photo: Kelvin Lister-Stuttard
12. SUB: Joe Worrall - 6/10
For Foster, 46 Marshalled the backline and defended the box well with some headed clearances on a rare league outing as Parker shuffled things after the red. (Photo by Alex Livesey/Getty Images) Photo: Alex Livesey