The Reds are held by the Canaries at Oakwell in the Sky Bet Championship.
Oli McBurnie's 6th goal for Barnsley in the first half was cancelled out by the impressive Josh Murphy after the break as the Reds' search for a home win continues.
Reds Head coach, José Morais made five changes once again ahead of this evening's match against the Canaries. Returns to the starting XI for Zeki Fryers and Andy Yiadom at full back, Adam Davies preferred to Nick Townsend in goal; Brad Potts was back from injury in midfield and Mamadou Thiam replaced Ryan Hedges out wide.
The first half was dominated by the Reds but clear-cut chances were hard to find, with the Norfolk visiting side reduced themselves to set-play opportunities and the odd counter-attack.
On one of those Norwich breaks, Liam Lindsay had to haul back the advancing Josh Murphy on halfway which saw him booked by referee Stephen Martin.
The first effort of note was a Brad Potts volley from 20 yards which finished a flowing Reds move that involved Potts, Kieffer Moore and Joe Williams. Great first-time passing and Potts' rocket of a shot whistled just a yard wide of Norwich 'keeper Angus Gunn's near post.
Williams was in the thick of it on the half hour mark when he received a Gary Gardner pass and fired a low shot straight at Gunn.
The match became stop-start for a while, very scrappy with neither side retaining possession well.
But the goal the Reds probably deserved on the balance of play arrived as we headed into first half stoppage time.
Yiadom burst forward on the right flank and whipped in a low inviting cross into the six yard box, Oli McBurnie got across his marker and hooked home a half-volley via the inside of the post despite Gunn's best efforts to keep it out.
It was the striker's 6th Reds goal in his 8th appearance and the last action of the half.
HALF TIME: Barnsley 1-0 Norwich
The Reds had a huge chance to double their lead just 8 minutes into the second half when Moore found his way into the box via McBurnie's through-ball, but the big man's first strike was blocked, his second from inside the six-yard box was fired straight into the 'keeper's legs. Williams' follow-up was gathered by Gunn in goal at the second attempt.
And just 30 seconds later another huge chance inside the box as Thiam wriggled into space, but his shot from six yards on the angle drifted badly wide. It had been a big 60 seconds, with the Reds failing to add what would have been the killer second goal.
Josh Murphy fizzed a long-range effort over on the hour mark, City's first effort of note all game.
Lloyd Isgrove replaced Thiam shortly after for the Reds.
By 70 minutes, the away side were on top and pressing hard for a leveller after a change in shape.
Murphy again went close, a thunderous, bending effort from 30-yards that missed by an inch.
Two minutes later and the goal they'd been threatening for over 10 minutes finally arrived as Murphy made it third time lucky when he fired in from an acute angle after some nervy Reds defending.
Gary Gardner had been busy in midfield but he picked up a yellow card when he followed through in a tussle with Marcus Maddison.
The Canaries brought on Wes Hoolahan on 81 minutes in place of Alex Tettey who was stretchered off after falling awkwardly.
Moore then ghosted towards the box, but as he looked to let fly from just inside the box, Grant Hanley put in a terrific sliding, blocked challenge.
Stevie Mallan replaced Williams with five minutes to play and his sweetly hit volley in the 90th minute flew inches wide of Gunn's goal.
Ex-Red Marley Watkins had been very quiet, he was subbed off in injury time to warm applause and it was City who had the last chance to win an even contest when Murphy fired over the bar from six yards with the goal at his mercy.
It's another tough one to take, but the Reds extend their advantage over the relegation zone to three points and host Millwall this Saturday.
FULL TIME: Barnsley 1-1 Norwich
Reds: Davies (GK); Yiadom, Jackson, Lindsay, Fryers; Williams (Mallan 85), Gardner, Potts; Thiam (Isgrove 60), Moore, McBurnie.
Unused: Townsend (GK), Pearson, Moncur, Bradshaw.