A spirited second half fightback wasn't enough to see the Reds come away with anything today.
The Reds Head Coach selected an unchanged XI for today's game, with the only change coming among the substitutes with Saidy Janko back on the bench in place of Ryan Williams.
The Reds had the first effort on target when Marley Watkins burst in off the right wing and put in a dangerous low ball that evaded everyone, leaving Norwich 'keeper Michael McGovern unsighted but the Northern Irish international grabbed the ball at the death before it crept into the bottom left-hand corner.
The game settled somewhat for the next 10 minutes before the hosts began to wrestle control of midfield.
Canaries midfielder Jonny Howson tried two efforts from 25 yards out in quick succession, with the first clearing Adam Davies' crossbar comfortably and the second effort was saved easily by Davies low down.
Alex Pritchard followed Howson by attempting to score from distance twice; his first being a right-footed curler that Davies caught with ease, but his next try went very close to giving the home side the lead as another curled effort on the right foot bent just beyond the far corner with Davies beaten.
Heckingbottom's men did find the net themselves on the half hour mark when an Adam Hammill cross made its way to Tom Bradshaw at the far post via Watkins, but as Bradshaw swept home the finish the assistant flagged for an offside.
Another flowing Reds move following a great tackle in midfield by Josh Scowen saw Hammill into the box on the angle, left-hand side, but the winger's low effort was saved well at his near post by McGovern.
Wes Hoolahan had to be replaced by Norwich soon afterwards, with Steven Naismith on in his place.
Bradshaw went close again, this time with a header that cleared the bar after Marc Roberts had headed a Hammill free-kick back across the six-yard box.
It was beginning to turn into the Hammill show, as the Scouse Magician dribbled past four men in style before winning a corner.
But then the sucker-punch. Right before the half-time break, after good defending in their own box, the Reds had time to clear their lines but Adam Armstrong's pass was intercepted and the Canaries saw Cameron Jerome pull a cross back for Jacob Murphy on the right-hand side and he moved onto the outside before rifling home, hard and low and into the bottom left corner beyond Davies' dive.
HALF TIME: Norwich City 1-0 Barnsley
Barnsley started the second half in brilliant fashion.
Within a minute of the restart, Yiadom's pull-back from the by-line was back-heeled towards goal by Hammill but McGovern somehow kept it out.
From the resulting corner, Angus MacDonald flicked a volley towards the near post which McGovern saved expertly, turning it behind for another corner.
Approaching the hour mark and Hammill and Matty James both tried from the edge of the box, but without reward. It was all Barnsley.
Adam Armstrong was replaced by Ryan Kent on 57 minutes.
The Reds' best chance of the game soon followed as Watkins found himself one-on-one with the 'keeper but his shot sliced wide when he needed to work McGovern at least.
Then came the sucker-punch. Norwich doubled the lead with a very rare attacking move. And it came about in extremely cruel conditions.
After an initial Davies save, the ball somehow ricocheted back in and MacDonald flicked the ball into his own net for 2-0.
Davies had to be at his best soon afterwards to thwart Jerome low down with a terrific save as Norwich looked certain to make it 3-0.
Alex Mowatt came on for Watkins in the 77th minute, Ryan Hedges then replaced Adam Hammill on 81.
The game was drawing to a close at this stage and Norwich brought on Graham Dorrans and Nelson Oliveira, replacing Jerome and Murphy.
Howson went close to making it a third for the Canaries after Dorrans slipped him through on goal, but his lovely deft effort was superbly headed behind by MacDonald on his own goal-line.
There was a late chance for Bradshaw to finally get the goal his work had deserved when he got on the end of a brilliant Gethin Jones cross but his cracking volley arrowed just over the Norwich bar from around eight yards out.
Kent summed up the Reds display when he somehow fired wide first time from about four yards out after a perfect cross by Hedges. The chances were there in the game, but the Reds couldn't take them.
It had been another good performance from Hecky's Reds, but their hosts ran out 2-0 winners regardless.
FULL TIME: Norwich City 2-0 Barnsley
Reds XI: Davies (GK); Yiadom, Roberts, MacDonald, Jones; Hammill (Hedges 81'), Scowen, James, Watkins (Mowatt 77'); Bradshaw, Armstrong (Kent 57').
Unused Subs: Townsend (GK), Jackson, Moncur, Janko.
Attendance: 26, 107.