Jacob Murphy reached double figures for the season just before the break to fire the Canaries ahead, while an own goal from Angus MacDonald midway through the second period settled the issue.
The well-deserved victory made it four points from six for caretaker boss Alan Irvine, who took charge after the sacking of Alex Neil eight days ago, but Norwich will need to maintain that sort of form for the remainder of the campaign to have any chance of breaking into the top six.
The hosts started off on the front foot, with young winger Murphy the main threat in the early stages.
He set up a decent chance for the Canaries, but no one could get their shot away, while he also got free down the right, only to fail to pick out Cameron Jerome in the six-yard box.
Jonny Howson then fired one straight at Adam Davies as the Canaries continued to have the better of it, while the keeper also gathered a well struck shot from Alex Pritchard.
It was all Norwich, and Barnsley had a lucky escape on 22 minutes when Pritchard curled another effort inches wide after an incisive home attack.
Davies then carelessly spilled a speculative long-range effort from defender Ivo Pinto, and was relieved when Murphy was flagged offside as he went to convert the loose ball.
At the other end Adam Hammill found the back of the net, but from a clearly offside position, while the same player fired in Barnsley's first shot on target, which was easily gathered by Michael McGovern.
The opening goal finally arrived a minute before the break, with the hosts deservedly going in front.
The Barnsley defence switched off as Jerome chased a hopeful punt forward and the striker had time to pick out an unmarked Murphy, who drilled a low shot into corner of the net from some 10 yards out.
The Tykes twice came close to equalising in the opening minute of the second period.
Hammill was unable to get enough on his flick to convert Andy Yiadom's cross into the six-yard box, while from the resultant corner Angus McDonald's close-range effort was well saved by McGovern.
Marley Watkins then pounced on a slip from Norwich skipper Russell Martin but, under pressure, he fired a shot well wide of the target.
It had been an encouraging start to the half from the visitors, but they nearly went two down on the hour mark when substitute Steven Naismith burst into the box, only to scoop his effort well over with just the keeper to beat.
City did stretch their lead on 70 minutes, however, with their second goal having a big slice of luck about it.
Keeper Davies, who seconds earlier had denied Naismith with a smart stop, also blocked Murphy's follow-up effort but the ball was deflected straight back into the net by covering defender MacDonald.
Jerome almost made it three after being put clean through by Naismith, but Davies put an excellent stop to deny him.
MacDonald then made a brilliant goal-line stop to keep out Howson's effort as Norwich comfortably saw out the game.