Second-half goals from Wes Hoolahan, Jamie Cureton, Sammy Clingam and Darel Russell secured a much-needed three points, but the all-round team performance was unrecognisable from Tuesday night's FA Cup exit.
Norwich kicked off attacking the Barclay End goal, but it was Barnsley with the first shooting chance which Maceo Rigters put wide.
Cureton, who was back from his loan spell with Barnsley, headed wide from Lee Croft's right-wing cross.
Diego Leon was booked for a foul on Clingan and was lucky to escape a second yellow for a foul on Croft.
After sustained pressure from the home side, Barnsley broke away and Rigters saw his shot blocked.
Russell had the first shot of the second half but it flashed wide of goal.
However, in the 55th minute, Russell's pass set up Hoolahan, who rounded Heinz Muller and found the net with an angled right-foot shot from six yards.
With 20 minutes to play, Cureton tried to lob Muller but the keeper managed to grab the ball.
Cureton was on the scoresheet five minutes later when he got between Darren Moore and the keeper and this time beat Muller with a well-judged right-foot lob.
Jon Macken's volley was blocked before substitute Matty Pattison's run into the Barnsley penalty area was blocked by Marciano van Homoet and Clingan beat Muller from the spot, sending him the wrong way with a firm right-foot shot to the keeper's right.
The other two City substitutes combined to set-up Russell for the fourth goal.
Arturo Lupoli found David Bell on the Norwich right and his cross was headed in from six yards by Russell, leaping at the far post.
The home fans were understandably rapturous in their applause for the team and the caretaker manager Bryan Gunn - the former Canaries keeper.