Norwich are still without a Premiership win but managed to earn a point despite keeper Robert Green's error at Manchester City.
Willo Flood put City ahead with a volleyed shot from outside the box, which slipped through Green's hands.
But Damien Francis equalised for Norwich after a defensive mix-up gifted him the chance to slot home.
Flood hit the post in the second half and Craig Fleming was lucky not to concede a penalty as Norwich held on.
Norwich, who had not scored in more than five hours of football on their travels, had their first chance of the game - and their best of the half - after just six minutes.
Darren Huckerby's free-kick found McKenzie in the penalty area, but the striker failed to connect with the ball.
It proved to be the visitors' last sight of goal for a while as City dominated, with Flood seeing plenty of the ball and making good use of it.
Norwich boss Nigel Worthington must have been watching with an envious eye as the 19-year-old continually linked up well with Nicolas Anelka and Shaun Wright-Phillips.
And Worthington's jealousy must have turned to rage when Wright-Phillips found Flood with a cross-field pass and the youngster's first-time volley embarrassed Green.
By contrast, Norwich - and Huckerby in particular - were finding it hard to get involved in the game.
But when they did find a way through, Francis saw his shot well saved by David James.
Fortunately for Norwich, their hosts were finding it equally difficult to get past Green, who had by now recovered from his earlier howler.
Wright-Phillips and Anelka were both denied by good saves as Kevin Keegan's new front pairing carved through the Canaries' defence.
With City well in control, and Norwich looking over-run in midfield, the hosts may have come out after the break feeling slightly complacent.
The slack attitude may be an explanation for the mess the City defence got themselves in just seconds after the re-start.
Danny Mills' backwards header and his team-mates' inability to clear the ball handed Francis the perfect chance to equalise and he made no mistake from just inside the box.
City, to their credit, came straight back and Wright-Phillips tested Green.
But there was a new belief about Norwich and more tenacity about their play which created chances for Francis, but he could not find the target.
At the other end, City were inches away from talking the lead after Wright-Phillips and Flood combined again but the Irishman saw his shot cannon back off the post.
City pushed for a winner and were unlucky when Anelka cut inside the defence only to see his goal-bound shot cleared off the line.
The ball rebounded back to substitute Robbie Fowler, who claimed handball as Fleming got in the way of his shot.
It appeared the defender was lucky not to concede the spot-kick, but it meant Norwich earned a point as they clung on.
Man City: James, Mills, Distin, Dunne (Onuoha 68), Jordan,
Flood, Sibierski, Bosvelt, McManaman (Fowler 81),
Shaun Wright-Phillips, Anelka.
Subs Not Used: Waterreus, Bradley Wright-Phillips, McCarthy.
Goals: Flood 11.
Norwich: Green, Edworthy, Fleming, Charlton, Brennan, Holt,
Jonson (Henderson 81), Francis, Huckerby,
McKenzie (McVeigh 87), Svensson.
Subs Not Used: Mulryne, Ward, Helveg.
Goals: Francis 46.
Ref: S Bennett (Kent).