With David Neilsen's introduction the Canaries play became more purposeful and the Dan's pace unsettled the visitors.
After 30 minutes he received the ball after good work by Clint Easton down the left, before cutting it back for Phil Mulryne whose shot was just wide of keeper Tony Warner's right hand post.
Twice more Neilsen's pace nearly unlocked the Millwall defence before he finally succeeded in the 43rd minute.
He cleverly controlled Mulryne's cross, rounded a defender, and fired a right foot shot past the despairing dive of Warner.
Millwall took only five second half minutes to find an equaliser, although Steve Claridge looked well off side, before lifting the ball over keeper Robert Green.
The Canaries regained the lead in the 59th minute when Steen Nedergaard delivered the perfect cross for Neilsen to flick his header past Warner.
Norwich continued to control the game, and it came as no surprise when they extended their lead after 72 minutes.
Mylryne floated a free kick to the far post where defender Darren Kenton rose to flick his header over Warner.
The Lions showed they were not going to lie down, but apart from Claridge's run down the right 13 minutes from time they couldn't penetrate the Canaries rearguard.