Substitute Jacob Bruun Larsen struck an unstoppable drive into the top corner as Vincent Kompany’s men recorded a 2-1 win at Kenilworth Road.
The result moved the Clarets up to 18th, having taken four points from their opening seven games.
But how has the result impacted on their survival odds? We take a look here by collating data from 25+ bookmakers to determine who is most likely to go down...
1. Up and running
LUTON, ENGLAND - OCTOBER 3: Connor Roberts of Burnley celebrates with team mates during the Premier League match between Luton Town and Burnley FC at Kenilworth Road on October 3, 2023 in Luton, England. (Photo by Marc Atkins/Getty Images) Photo: Marc Atkins
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