Heading into the clash with the confidence of having toppled leaders QPR last time out, the Canaries enjoyed a dream start as the prolific Grant Holt's sixth goal in as many games gave them an early lead.
But Middlesbrough have been showing signs of life themselves recently, having claimed a creditable draw at Leeds on New Year's Day, and they grabbed a deserved share of the spoils through Russell Martin's own goal.
Despite going into the game on the back of three successive victories, City manager Paul Lambert opted to make three changes to the XI that overcame the Hoops on Saturday.
It did not affect the Canaries, though, and they found themselves ahead in just the 12th minute.
Neat build-up play in midfield saw Martin drive up the field before picking out Aaron Wilbraham with a hopeful aerial ball.
The former MK Dons man, playing only his second match since moving to Carrow Road last week, rose well and flicked onto Holt, who, having ghosted in behind David Wheater, finished from the tightest of angles.
Not content with one, the visitors pushed for a second and nearly got it instantly but Holt and Owain Tudur Jones saw goal-bound efforts blocked.
Boro have been looking increasingly resilient under Tony Mowbray in recent times and they soon restored parity, albeit in somewhat fortuitous circumstances as Martin unfortunately deflected Julio Arca's ball past his own keeper.
That seemed to spur the home side on and they could have taken the lead when Joe Bennett hit just wide from 25 yards.
The game entered a lull thereafter, with the two sides battling for the initiative.
Norwich could have gone into the break ahead, but, after capitalising on a mistake from Matthew Bates, Wilbraham saw his excellent effort turned round the post by Jason Steele.
Lambert decided to bring on Chris Martin at the interval as his side searched for an all-important second goal and the move almost paid instant dividends as the forward saw an effort blocked.
However, as the game wore on, chances became increasingly few and far between, with both sides seemingly content to play neat football, rather than seize control.
It was Middlesbrough who looked the more likely to go on and claim the points in the closing stages, with John Ruddy brilliantly denying Barry Robson before Kris Boyd headed just wide from the resulting corner.
Wheater thought he had earned his side the win with five minutes to go, but saw his header ruled out for a push.
Julian Hoyte then hit the post for the hosts as the Canaries were left hanging on for dear life at the end.