Burnley caretaker boss Mike Jackson warned "it is not mission accomplished" after the Clarets climbed out of the relegation zone to put their Premier League fate in their own hands.
Nick Pope made a string of fine saves to frustrate Aston Villa and help secure a hard-earned point that saw Leeds United drop to 18th before what is certain to be a tense final day on Sunday.
Burnley and Leeds are now locked on 35 points, but the Clarets' -18 goal difference is far superior to Leeds' -38. While Jackson's side entertain 12th-placed Newcastle at the weekend, Leeds are at 11th-placed Brentford.