Victories against Liverpool and Aston Villa have lifted the Clarets nine points above the relegation zone and into 15th.
Below Sean Dyche’s men sit Newcastle United, Brighton & Hove Albion, Fulham, West Brom and Sheffield United.
We’ve checked out the latest Premier League relegation odds with the bookmakers to see how they’re rating Burnley’s chance of remaining in the division.
Scroll and click through our gallery to see how the bookies view the current relegation picture:
13. West Bromwich Albion - 1/6
Under Sam Allardyce's reign, the Baggies have concerned a staggering 17 home goals in four games at the Hawthorns - but you can never rule a Big Sam team out, can you? Photo: ADRIAN DENNIS
14. Sheffield United - 1/10
Despite the Blades' shock 2-1 win at Premier League title chasing Manchester United, the bookmakers are struggling to see how Chris Wilder's men can pull off the impossible. They remain 10 points adrift but never say never... Photo: DAVE THOMPSON