Birmingham City continue to stutter at home and failed for the fifth game to win at St. Andrew's when they were booed off the pitch by their frustrated fans.
Birmingham stormed into a tenth minute lead through Morrison following smart play by Darren Anderton and Emile Heskey.
But their disappointment was that they did not consolidate their early lead when they were thwarted by goalkeeper Robert Green.
Everything looked very rosy for Birmingham when Anderton floated in a cross which Heskey headed goalwards only for Green to finger-tip his effort onto the bar.
But the ever alert Morrison was on hand to slot the ball home for his first Premiership goal of the season which could quite conceivably be the turning point for both the striker and the Midlands club.
Morrison might well have had a first half hat-trick but Green thwarted the Republic of Ireland international with two smart saves just before the break.
Heskey twice went close to increasing Birmingham's lead but was off-target on each occasion and the let-offs certainly gave Norwich fresh impetus to take the game to Birmingham.
Not for the first time this season Birmingham lost their way in midfield and suddenly became vulnerable in the second half.
Although Robbie Savage continued to charge around the pitch Birmingham began to pay a heavy price for their first half domination and began to flag as Norwich launched some positive attacks with David Bentley catching the eye.
In the 62 minute, much to the delight of the travelling Norwich fans and amazement of the home supporters, Huckerby grabbed a hard earned equaliser.
Maik Taylor was badly at fault when he failed miserably to cut out a long cross from the left. Bentley gained possession and carefully guided his cross to the far post where Huckerby had little difficulty recording his fourth goal in the Premiership.
This goal knocked Birmingham completely off course as they struggled to regain their earlier composed attacking play. Instead they lost the midfield battle and with Matt Svensson a major inspiration, Norwich were more than worth their latest point.
Huckerby went close to snatching a dramatic winner, while Savage was angry with himself when a close-range header lacked power to beat Green.
Man of the Match: Mathias Svensson - The big Swede led the Canaries frontline effectively and troubled the Blues defence throughout the game.