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:
1. Everton - 1000/1
Carlo Ancelotti's men are closer to top-of-table Manchester City than they are to the relegation places. With 33 points from 18 games, it's safe to say Everton have no chance of being relegated, as reflected in the bookies' odds. Photo: Michael Regan
2. Arsenal - 1000/1
A few weeks ago, Arsenal's relegation odds would have been very, very different. However, five wins out of six games have propelled Mike Arteta's men up the table. Photo: Pool
3. West Ham United - 750/1
David Moyes' men are arguably the surprise package of the season. Heavily tipped for relegation at the beginning of the campaign but 20 games in, and they're in the top four. Photo: CLIVE ROSE
4. Southampton - 250/1
Ralph Hasenhuttl's side are another who have performed above expectations so far. After 19 games, they've already accumulated 29 points. Photo: FRANK AUGSTEIN