Jamie Cureton, given the captain's armband for the day, scored the only goal of the game, which was enough to lift the Canaries into the top half of the Championship table.
The home side kicked off attacking the Barclay-End goal, but made little headway against the tough-tackling Tykes until the 12th minute when Ryan Bertrand's left-wing cross was headed over by Ched Evans
Daniel Nardiello saw his shot cleared off the line by John Otsemobor after David Marshall had been outsmarted on the edge of the penalty area.
Evans and Lee Croft had shots blocked before Croft's deflected right-wing cross in the 26th minute fell to Cureton.
He marked his return to the starting line-up with a trademark finish from 16 yards, his right-foot shot beating Luke Steele low to his right.
Four minutes before the interval Anderson de Silva was stretchered off to be replaced by Marciano van Homoet.
Five minutes after the break, the impressive Alex Pearce, on loan from Reading, got his head to Darren Huckerby's free-kick, but the ball was deflected over the bar for a corner.
Croft set up Evans but his shot went a foot wide of goal, before Diego Leon and Nardiello were replaced by Kayode Odejayi and Jon Macken, who brought a good save from Marshall with a snap shot seconds after coming on.
Huckerby set up Croft, who fired wide and, as the game entered three minutes of added time, Huckerby again was the provider, but this time Steele beat away Croft's well-placed shot.