The Canaries ended up sneaking home 3-2 after appearing to be in total command with a 3-0 lead at half-time.
Goals from Gary Hooper, Kyle Lafferty and Cameron Jerome, together with a penalty save from John Ruddy, made it a miserable opening period for the visitors.
But they then made a game of it by scoring twice in three minutes around the hour mark through Alex Revell and Kadeem Harris and might have come away with a draw in the end.
New Norwich manager Neil was given a rousing reception before kick-off and his team responded to a cracking atmosphere by dominating the early stages.
It took an excellent one-handed stop from Cardiff keeper Simon Moore to keep out a Hooper snap shot on eight minutes – but he could nothing to prevent the same player from opening the scoring on the quarter-of-an-hour mark.
Nathan Redmond’s cross from the right found the head of Jerome and he nodded the ball on for his strike partner to convert from close range at the back post.
Cardiff might have equalised five minutes later when a corner was missed by Norwich keeper Ruddy and Sean Morrison failed to convert from close range.
But the hosts looked the stronger side and it needed another good stop from Moore to keep out a fiercely struck shot from Gary O’Neil.
The Canaries then caught the visitors on the break to make it 2-0 on 25 minutes. The ball fell to Lafferty in oceans of space out on the left and had plenty of time to pick his spot, with his curling shot finding the back of the net via the far post.
The Bluebirds should have been back in it almost immediately when Carlos Cuellar was adjudged to have tripped Adam Le Fondre in the box but Ruddy made a superb save to his left to deny Peter Whittingham from the spot.
The penalty had come after a swift Cardiff break – and the Welsh side again caught Norwich short five minutes from the interval, only for Revell to scoop the ball over from inside the six-yard box.
The points appeared to be wrapped up in stoppage-time when Norwich scored their third.
A buccaneering run from Russell Martin took the defender deep into the visitors’ area and, when his effort was blocked, Jerome was on hand to steer home his 14th goal of the season from close range.
Norwich continued to go hunting for goals after the break and Redmond saw his rising drive come back off the crossbar while Jerome’s far post header went just wide a couple of minutes later.
Cardiff kept battling away though and got one back on 61 minutes. Whittingham picked out Revell at the back post and the big striker coolly side-footed home to open his account for his new club.
It was a goal the visitors deserved as it had not been a one-sided game by any means, and they were right back in it a couple a minutes later when they got a second.
A long punt forward from keeper Moore deceived the home defence and substitute Harris nipped in to lob the ball over Ruddy.
It needed another good save from Moore to prevent Redmond from making it 4-2 while substitute Wes Hoolahan fired just over as the hosts started to regain the upper hand.
Cardiff still posed a threat however and Revell went close to completing what would have been a remarkable comeback 10 minutes from time with a header that drifted just wide.