Saturday lunchtime's result means that the Tykes will now meet Swansea City in the semi-finals of the play-offs as they bid to round off a remarkable 2020-21 campaign with promotion to the Premier League.
Whether too much can be read into the result remains to be seen, but Valerien Ismael will doubtless have been thrilled by the way his own game-plan and his players' intensity caused a visiting side who have won the division at a canter so many problems - for 45 minutes at least.
There was absolutely nothing riding on the outcome of the contest for the Canaries, though they are an extremely well-oiled machine and struggled to get out of their own half during an opening period which Barnsley had much the better of.
The hosts initially threatened when Conor Chaplin brought the ball down on his chest and shot over the top before Jasper Moon saw an attempt from a very similar position on the edge of the City box held by Tim Krul.
Chaplin's deflected free-kick was then fisted clear by the Dutch international goalkeeper as the Reds continued to look the more likely.
And they edged in front on 24 minutes after Canaries defender Andrew Omobamidele was caught in possession deep inside his own half and outmuscled by Carlton Morris.
The former Norwich striker advanced towards goal then slipped the ball across from the left side of the penalty area for Cauley Woodrow to fire into an empty net.
City are however champions for a reason and showed their class in drawing level within two minutes of falling behind, Max Aarons getting forward down the right and delivering an inviting cross which Emiliano Buendia nodded into the bottom corner.
Undeterred, Barnsley kept coming and both Chaplin and Woodrow unleashed efforts from useful positions that were just too close to Krul.
But, the reward for a very positive first 45 arrived two minutes before the interval as Chaplin eventually found his range.
Callum Styles whipped in a delicious cross from the left and the diminutive attacker directed an excellent close-range header beyond the despairing dive of Krul.
Barnsley began the second period brightly and pressing for a third, though they were caught short at the back as Norwich launched a devastating 54th-minute counter-attack to draw level for a second time.
The visitors made swift progress down their right, Buendia then pulling the ball back for Todd Cantwell, who in turn picked out the unmarked Adam Idah to blast into the roof of the net less than two minutes after arriving from the substitutes' bench.
There wasn't too much in the way of goalmouth action during the period which followed, Jordan Hugill's powerful header from Mario Vrancic's glorious left-wing free-kick as close as either side came.
And it took until the 84th minute for a clearer opportunity to materialise, Vrancic and Kieran Dowell combining to send Buendia clean through on goal, only for the Argentinia to shank his finish wide of the upright.
Barnsley: Collins; Sibbick (Kitching 82), Helik, Andersen; Brittain, Moon (Williams 66), Palmer, Styles; Chaplin (Frieser 55), Woodrow (Dike 55), Morris (Adeboyejo 55). Unused substitutes: Walton, Oduor, Halme, Sollbauer.
Norwich City: Krul; Aarons, Omobamidele, Hanley, Giannoulis; Tettey (Sorensen 87), McLean (Idah 52); Buendia, Francis, Cantwell (Hernandez 87); Hugill (Dowell 72). Unused substitutes: Nyland, Placheta, Quintilla, Stiepermann, Mumba.