The visitors came into the clash just four points off the top six while Blues sat a more modest 11 away.
HowBlues' run of three games without a win in all competitions was extended to four while Alex Neil's Canaries failed to respond to last week's 2-1 home defeat by Brentford with victory in the midlands.
Norwich had more possession early on but Blues managed the first two chances, with David Cotterill's fourth-minute shot from the edge of the box being saved by John Ruddy at the second attempt.
Demarai Gray's flicked effort, stretching to reach Stephen Gleeson's teasing ball forward, was also held by the Canaries goalkeeper.
Lewis Grabban's volley over Darren Randolph's crossbar was one of Norwich's few early openings
Former Blues winger Nathan Redmond tested Randolph with a powerful attempt from the right but the Blues stopper kept it out at full stretch as Norwich moved up a gear.
Two minutes into the second half, the largely indifferent Lloyd Dyer carved out a good chance for Blues when he jinked his way into the box from the left before seeing his close-range shot saved well by the imposing figure of Ruddy.
Norwich looked the better side, however, and the tricky Redmond whipped over a decent cross from the right which captain Russell Martin blasted over the bar with his right foot in the 56th minute.
For all their pace, Blues were seemingly missing their in-form playmaker Andrew Shinnie, rested by manager Gary Rowett with winger Gray playing a more central role.
Norwich came close in the 66th minute when Martin was again in the right spot, but this time the defender saw his header cleared off the line by Blues right-back Paul Caddis on the post.
Rowett then decided to throw Shinnie on for Dyer - while opposite number Neil introduced former Blues striker Cameron Jerome in place of Grabban.
Redmond looked Norwich's only likely candidate to spark a winner
Blues, too, continued to probe, but Gray's low cross was just too much of an angle for Shinnie to score from while Redmond saw a shot saved at the other end.
Blues substitute Nikola Zigic fired wide on the turn as a largely uneventful clash reached a tense finale
Source : PA