Jose Morais was denied a second victory as Barnsley manager thanks to Josh Murphy’s late equaliser for Norwich.
Oli McBurnie had given the Reds a deserved lead on the stroke of half-time, but they were pegged back, although the point they did secure moved them three clear of the relegation zone.
The Reds - now without a win on home soil in 10 attempts - had made an encouraging start.
McBurnie was thwarted in the opening couple of minutes as his strike was bravely blocked by Ivo Pinto after Joe Williams had played a precise through-ball.
Gary Gardner was busy in the Reds’ midfield, and he took aim from 30 yards following some terrific hold-up play from Kieffer Moore. The shot flew narrowly over the top.
The hosts played neat one-touch football, and after 20 minutes they came close to breaking the deadlock. McBurnie teed up Brad Potts, only for the midfielder’s crisp shot to whistle inches past the post.
The Canaries appeared a little stunned as the second quarter approached, though James Maddison proved just what a threat he can be when he fizzed an effort wide, via a deflection.
Back came the Reds, and Moore met Andy Yiadom’s cross, only to see his headed effort saved by City ‘keeper Angus Gunn.
Williams - another who was impressing across the Reds’ midfield - was then denied by the alert Gunn.
Just when it was looking as though the Reds were to head into the interval without reward, they grabbed the goal their performance had deserved when McBurnie struck seconds before half-time.
The Swansea loanee was perfectly placed to tuck home Yiadom’s cross, registering his sixth Reds goal in seven games.
Morais’s side kept their foot on the gas in the second period’s early exchanges.
They fluffed a terrific double chance in the 52nd minute.
Moore saw an initial strike beaten away by Gunn, with the rebound from Williams also somehow being kept out by the Norwich stopper.
Mamadou Thiam also caught sight of goal, dragging a shot off target after he had latched on to another decent delivery from the impressive Yiadom.
The Canaries had been second best throughout the game, but they almost grabbed themselves a shock leveller on the hour mark. Murphy found space in the box, only to lash an effort wide.
That threat averted, the Reds swiftly got themselves back on the front foot.
Potts made inroads into the Canaries’ box, but a cool finishing touch was missing and another chance went begging.
The numerous missed chances went on to cost the Reds, as the Canaries evened it up with 19 minutes to go.
Murphy notched, tucking home from close range as he darted in to meet James Husband’s pinpoint cross.
Barnsley (4-3-3): Davies; Yiadom, Jackson, Lindsay, Fryers; Potts, Gardner, Williams (Mallan, 86); Thiam (Isgrove, 60), Moore, McBurnie.
Subs not used: Townsend, Bradshaw, Moncur, Cavare, Pearson.
Norwich (4-4-2): Gunn; Pinto, Hanley, Zimmermann (Hernandez, 55), Klose; Husband, Tettey (Hoolahan, 81), Vrancic, Maddison; Murphy, Watkins (Srbeny, 90).
Subs not used: McGovern, Reed, Raggett, Lewis.
Referee: Stephen Martin (Staffordshire).