Miguel Mostto grabbed his first goal in English football as Barnsley extended their unbeaten run to seven matches.
The Peru international reacted well when Lewin Nyatanga's second-half header came back off the crossbar to side-foot home a deserved equaliser.
Earlier Andy Gray had lashed home his eighth goal of the season in the 11th minute when he pounced on a loose ball.
In the closing stages Wade Elliott went close for Barnsley, while Tykes keeper Heinz Muller saved from Chris McCann.
Barnsley boss Simon Davey:
"There's character in the side and the players don't know when they're beaten.
"In the second half I thought we came back into it and could probably have
gone on to win."
Burnley manager Steve Cotterill: "I thought in the first half we were excellent and could have been three or four goals to the good.
"The players are a little disappointed but I thought it was an excellent advert for the Championship."
Barnsley: Muller, Foster, Souza, Nyatanga, Werling, Campbell-Ryce (Ricketts 84), Howard, McCann, Devaney, Mostto, Odejayi.
Subs Not Used: Colgan, Kozluk, Togwell, Coulson.
Goals: Mostto 71.
Burnley: Kiraly, Alexander, Caldwell, Carlisle, Jordan, Elliott, Spicer, McCann, Mahon (Lafferty 69), Akinbiyi (Jones 85), Gray.
Subs Not Used: Jensen, James O'Connor, Unsworth.
Goals: Gray 11.
Ref: Lee Probert (Wiltshire).