The hosts spurned numerous chances in a tense first half before Howson surged from midfield to fire a sublime left-footed strike beyond keeper David Forde.
Gary Hooper doubled Norwich’s lead with a penalty just before the break after Cameron Jerome was felled by Alan Dunne, before Wes Hoolahan made it three and Howson scored his second on the hour.
A stunned Millwall found enough resilience to claim a goal back after Diego Fabbrini won a penalty that Lee Gregory converted, but it was too little too late to ease the pressure on beleaguered manager Ian Holloway.
After sustained Norwich pressure for the first 20 minutes, Millwall began to respond, as Jos Hooiveld saw his powerful volley blocked by Carlos Cuellar before Ricardo Fuller struck team-mate Martyn Woolford with another effort.
The lively Fuller continued to threaten as first Cuellar and then Martin Olsson clumsily fouled the striker on the edge of the area, but the hosts squandered both opportunities from either side of the box.
The hosts’ wastefulness was duly punished in the 38th minute when Howson surged through midfield and struck an exquisite drive beyond Forde from outside the area to give Norwich the lead.
While Howson’s goal was slightly harsh on Millwall, the hosts had themselves to blame for Norwich’s second on the stroke of half time.
Graham Dorrans’ long-range effort was saved well by Forde, only for Alan Dunne to needlessly fell Jerome as the striker went to retrieve the rebound, with Hooper firing the resulting penalty straight down the middle.
Norwich had barely broken sweat in establishing a two-goal advantage and had a chance to make it three soon after the restart but Jerome headed Olsson’s cross straight at Forde.
Yet it was not long before the visitors effectively ended the contest as a slip by Millwall’s Sid Nelson was capitalised on ruthlessly by Hoolahan, who drove a left-footed strike beyond Forde on 57 minutes
And just three minutes later, the Canaries claimed a fourth all too easily as Jerome broke down the left before calmly delivering the ball across the box for Howson to slot into the empty net.
The hosts were now conceding chances with alarming regularity as Jerome went close twice before Dorrans struck the inside of the right post after Hoolahan found the West Brom loanee unmarked on 68 minutes.
The hosts claimed a goal back in the 82nd minute as Fabbrini drew Gary O’Neil into a foul in the area and substitute Gregory struck the penalty into the bottom-right corner.