Scott Parker’s side put up a spirited display against the Blues, but ultimately came up short as they suffered their third straight defeat to slip into the bottom three.
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.
The Burnley Express has launched a new WhatsApp channel to bring the latest news, analysis and team & injury updates directly to your phone. Simply click this link to join our Burnley Express WhatsApp channel.
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?
Your next Burnley FC read: 'Incorrect restart': Dermot Gallagher's view on Burnley's penalty shout against Chelsea
1. 1
Burnley fans inside Turf Moor for the Premier League fixture with Chelsea. Photo: Kelvin Lister-Stuttard Photo: Kelvin Lister-Stuttard
2. 2
Burnley fans inside Turf Moor for the Premier League fixture with Chelsea. Photo: Kelvin Lister-Stuttard Photo: Kelvin Lister-Stuttard
3. 3
Burnley fans inside Turf Moor for the Premier League fixture with Chelsea. Photo: Kelvin Lister-Stuttard Photo: Kelvin Lister-Stuttard
4. 4
Burnley fans inside Turf Moor for the Premier League fixture with Chelsea. Photo: Kelvin Lister-Stuttard Photo: Kelvin Lister-Stuttard