The Clarets were unable to capitalise on a strong first-half, even going in behind courtesy of Pedro Neto’s back post header.
The hosts then struggled to put Chelsea under pressure during the second-half, which made for a muted atmosphere inside Turf Moor, before Enzo Fernandez added a late second.
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Our photographer Kelvin Lister-Stuttard was on hand to snap the Clarets fans on the terraces.
Can you spot yourself in our gallery of fan pictures?
Burnley fans inside Turf Moor for the Premier League fixture with Chelsea. Photo: Kelvin Lister-Stuttard
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Burnley fans inside Turf Moor for the Premier League fixture with Chelsea. Photo: Kelvin Lister-Stuttard Photo: Kelvin Lister-Stuttard
Burnley fans inside Turf Moor for the Premier League fixture with Chelsea. Photo: Kelvin Lister-Stuttard
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Burnley fans inside Turf Moor for the Premier League fixture with Chelsea. Photo: Kelvin Lister-Stuttard Photo: Kelvin Lister-Stuttard
Burnley fans inside Turf Moor for the Premier League fixture with Chelsea. Photo: Kelvin Lister-Stuttard
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Burnley fans inside Turf Moor for the Premier League fixture with Chelsea. Photo: Kelvin Lister-Stuttard Photo: Kelvin Lister-Stuttard
Burnley fans inside Turf Moor for the Premier League fixture with Chelsea. Photo: Kelvin Lister-Stuttard
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Burnley fans inside Turf Moor for the Premier League fixture with Chelsea. Photo: Kelvin Lister-Stuttard Photo: Kelvin Lister-Stuttard