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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5. Lucas Pires - 6/10
His first Premier League start was going so well before he was shown a straight red, defending on the front foot and delivering some dangerous corners (Photo by George Wood/Getty Images) Photo: George Wood
6. Florentino Luis - 6/10
Fortunate to get away with an early mistake when he was caught in possession, but otherwise did fairly well breaking up possession. Photo: Kelvin Lister-Stuttard Photo: Kelvin Lister-Stuttard
7. Josh Cullen - 7/10
His usual steady display, battling right until the very end. Saw one effort comfortably saved and produced a couple of teasing crosses into the box. (Photo by George Wood/Getty Images) Photo: George Wood
8. Lesley Ugochukwu - 6/10
A bizarre decision to extend his two arms for the penalty, which he can have no complaints with. Threatened early on with his powerful runs through the centre of the pitch. Photo: Kelvin Lister-Stuttard Photo: Kelvin Lister-Stuttard