It means that while Brian Laws’ side move above Hull they remain in the relegation zone. Tuncay opened the scoring for Stoke in the 23rd minute but Burnley rallied in the second half.
Laws, though, is finding it hard to make an impact since replacing Owen Coyle as manager in January.
This was his ninth league match in charge and they have won only one. Next up are fellow strugglers Wolves on Saturday – another massive game.
Stoke took the lead following a long throw from Rory Delap. It was flicked on by Mamady Sidibe to Tuncay, who headed home.
Burnley came under pressure in the 31st minute when Matthew Etherington released Delap, only for Graham Alexander to show good positioning to block his shot.
Etherington then set up Tuncay in the area but his first touch was poor and Leon Cort was able to get the ball away. Burnley hit back and Eagles delivered a cross to Paterson at the back post in the 39th minute. However he showed a lack of confidence and sent his effort into the side-netting.
Stoke responded and Etherington latched on to a good ball from Andy Wilkinson and delivered it into the area – but Cort was able to clear.
Burnley, however, made a bright start to the second period and Eagles latched on to a pass from Nugent.
He skipped forward to the edge of the area only to go to ground following a challenge from Delap.
Eagles appealed for a free-kick but ref Howard Webb would have none of it and allowed play to continue.
Burnley stunned Stoke by drawing level in the 52nd minute with a goal out of nothing. Paterson turned Collins inside out before delivering a superb cross deep into the area.
Nugent was the first to react and left Sorensen stranded with a powerful header – his sixth goal for the club.
It was an open game now with both sides going for the win, rather than settling for a point.
Etherington tried to release Wilkinson in the 82nd minute but goalkeeper Brian Jensen anticipated, then a minute later substituteDave Kitson made space for himself before rattling in a shot which tested Jensen.
Burnley came close to getting the winner in the closing moments with Eagles sending a shot over the bar.
BURNLEY: Jensen, Mears, Carlisle, Cort, Fox (Jordan 77), Paterson, Alexander, Cork (McDonald 46), Eagles, Nugent, Thompson (Elliott 71). Subs Not Used: Weaver, Duff, Blake, Bikey. Booked: Carlisle, McDonald. STOKE: Sorensen, Wilkinson, Huth, Abdoulaye Faye, Collins, Lawrence (Pugh 63), Whitehead, Delap, Etherington, Sanli (Moult 85), Sidibe (Kitson 63). Subs Not Used: Begovic, Amdy Faye, Davies, Lund. Goals: Sanli 23. Att: 20,323 Ref: Howard Webb (S Yorkshire).