The Iron had got the better of the Lions in their previous five meetings, including an epic 2009 League One play-off final.
But the south Londoners got their own back in style thanks to Henry's first-half cracker and two late Morison strikes to make it an unhappy 40th birthday for Scunthorpe manager Ian Baraclough.
Staff at The Den worked round the clock to beat the icy conditions and ensure the match went ahead - and the Millwall players did not freeze in front of the TV cameras.
They should have gone ahead in the 14th minute when Morison chased a long clearance and outpaced the Scunthorpe defence.
The former Stevenage striker prodded the ball past Iron goalkeeper Joe Murphy from a tight angle, but it rolled across goal and wide of the far post.
But the hosts did not have to wait long to make the breakthrough as, in the 23rd minute, Henry strode unchallenged into the visitors' half.
As the defenders backed off, Henry unleashed a low drive from 25 yards which zipped past Murphy and into the corner of the net for the winger's first goal in more than a year.
Scunthorpe could have hit back moments later when Rob Jones met a cross from Eddie Nolan but the defender put his header wide.
But Millwall had the chances to be out of sight by half-time with Morison looping a header onto the top of the net and Calvin Andrew nodding Morison's cross over.
At the start of the second half Lions chief Kenny Jackett threw on new loan signing Josh McQuoid, the young striker who hit the headlines last month with two hat-tricks in a week for Bournemouth.
And McQuoid should have marked his debut with a goal on the hour mark, but he headed Jason Puncheon's cross wide from just six yards out.
With the score at 1-0 Scunthorpe always had a chance to get something out of the game.
But they were a huge disappointment and rarely threatened - Josh Wright's shot which flew miles over the crossbar was the sum total of their efforts after the interval.
Instead, it was Millwall who went further ahead with nine minutes remaining when Morison charged into the area, jinked past Jones and toe-poked the ball past Murphy from the tightest of angles.
And five minutes later Morison took his tally for the season to 10 when he lashed a half-clearance back past Murphy from the edge of the box to wrap up the win.