The Clarets were unable to arrest their winless home form, which now stretches to 14 league games, as the Canaries settled for a point, which brought an end to their run of 16 successive defeats in the top flight.
Sean Dyche's side, who have now failed to beat the last six promoted sides they have faced on home turf, enjoyed the lion's share of possession and territory during a drab affair, but failed to test goalkeeper Tim Krul.
Referee Kevin Friend dished out the yellow cards and waved away numerous penalty appeals in an untidy first half, which saw the visitors go closest to scoring when Max Aarons pulled an effort wide of the far post.
Daniel Farke's side also went close after the interval. Jay Rodriguez unlawfully halted Ozan Kabak's run through the middle and Nick Pope, who missed out on selection for Gareth Southgate's England squad, had to be at his best to divert Mathias Normann's set-piece to safety.
Krul, an ex-international team-mate of Erik Pieters, beat away baptised the second half with a save from McNeil, who would later squander a golden opportunity to wrap up the points when failing to convert substitute Johann Berg Gudmundsson's cross.
Rodriguez, who had replaced Matej Vydra before the break, failed to connect with the goal at his mercy once Krul had attempted to cut out a cross before defender Matt Lowton powered a header over from Josh Brownhill's delivery.
Here are the ratings.
Referee Kevin Friend dished out the yellow cards and waved away numerous penalty appeals in an untidy first half, which saw the visitors go closest to scoring when Max Aarons pulled an effort wide of the far post.
9. Josh Brownhill 5.5
A bundle of energy in the middle of the park, but early booking took the sting out of his display. Broke play up well when Norwich had turned over possession, picked out team-mates in-between the lines, and almost set up the winner with a wonderful give and go late on.
10. Matej Vydra 5.5
Deserved a penalty, or even two, when wiped out by Krul and later tripped inside the box by Hanley. His movement off the ball disjointed City's back three, he got on the ball in the inside channels, and opened things up, but injury ended his involvement prematurely.
11. Chris Wood 4.5
Largely anonymous. While the Clarets played to Norwich's strengths - with the three centre backs mopping everything up in the air - the Kiwi striker failed to compete. Didn't show enough strength or desire on or off the ball as the game passed him by.
12. Jay Rodriguez 5.5
Not afraid to get stuck in and ruffle a few feathers among the away side's defensive line. Dropped deep to show for the ball, while holding it up to allow his team-mates to get up the pitch, but squandered a huge opportunity to score with the goal at his mercy.