Jon Macken saw his early penalty saved by Norwich keeper David Marshall as bottom-placed Barnsley earned only their fourth point of the season.
Macken's spot-kick was tamely struck and easily saved after Matthew Pattison had handled in the area.
Soon after, Tykes striker Diego Leon struck a post with team-mate Jamal Campbell-Ryce also going close.
Norwich started to come into the game and Antoine Sibierski saw his firm header well saved by Heinz Muller.
Barnsley manager Simon Davey: "Our first-half performance was fantastic and we should have gone in three or four up.
"The players were fantastic and I couldn't have asked for any more from them.
"The lads are working 100% and there's a belief in the dressing room that we can turn things round. There's a platform for us to build on and we have to turn draws into wins."
Norwich manager Glenn Roeder:
"We can play a lot better, but when we don't play well it's nice to dig out a point, 'cause we've had to really scrap for that point.
"I don't like it when a team starts quicker than we do, and Barnsley did that right from the first few seconds.
"Their guy had a tremendous David Beckham-style shot, I don't know how Marshy back-peddled so quickly to tip it over."
"They made it difficult for us to play but it's a good sign when you don't play well and still pick up a point.
"If Barnsley play like that, I'm sure they'll get away from the bottom of the table. You have to pat them on the back for their performance."
Barnsley: Muller, Foster, Moore, Guedes, Kozluk, Campbell-Ryce, Colace (Devaney 69), De Silva, Leon, Hume, Macken (Odejayi 73). Subs Not Used: Steele, Hassell, Mostto.
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