Andrew Morrell scored in injury-time to earn Blackpool a draw, minutes after Ade Akinbiyi thought he had scored the winner for Burnley.
Burnley went ahead when Steve Jones scored with a low strike after collecting a cross from Robbie Blake.
Blackpool equalised when Wesley Hoolahan scored a penalty after Clarke Carlisle fouled on Morrell.
Substitute Akinbiyi put the Clarets ahead from six yards after 85 minutes before Morrell's left-foot strike.
Burnley boss Steve Cotterill:
"Two individual mistakes cost us but it's a team game and we let the ball come into our penalty area far too easily. What happens sometimes leaves a bitter taste.
"I don't think we deserved to win the game so a draw was a fair result.
"We weren't good enough today and that's why we didn't win. We need to do better collectively, generally our defending was pretty good but we haven't defended well as a team."
Blackpool manager Simon Grayson:
"We try and play the right way. The lads just kept on going and got the result we fully deserved.
"It was a cracking game with a fantastic atmosphere and some good football and full credit to the players as they never know when they are beaten."
Burnley: Jensen, Duff, Caldwell, Carlisle, Jordan, Elliott (Spicer 89), Alexander, McCann, Harley (Jones 46), Blake (Akinbiyi 76), Gray.
Subs Not Used: Kiraly, Unsworth.
Goals: Jones 52, Akinbiyi 86.
Blackpool: Rachubka, Barker, Jackson, Evatt, Crainey, Hoolahan, Southern (Flynn 88), Fox, Taylor-Fletcher (Welsh 62), Parker (Burgess 71), Morrell.
Subs Not Used: Vernon, Gorkss.
Goals: Hoolahan 73 pen, Morrell 90.
Ref: Mike Dean (Wirral).