The former Stevenage striker, a reported target for Hull boss Nigel Pearson, opened his account early in the first half and Kevin Lisbie doubled the lead before the break.
Seven minutes into the second half Morison capitalised on some more poor defending and Liam Trotter added a fourth as the Tigers' travel sickness showed no sign of clearing up.
They have now gone 17 months and 25 matches since their last league win on the road, against Fulham back in March 2009.
Newly-promoted Millwall, by contrast, remain a team to be feared down at The Den and are now unbeaten in their last 18 home games - form which should see them flourish in the higher division this term.
Full of confidence following their 3-0 opening-day win at Bristol City, the Lions went ahead in the 14th minute when James Henry swung in a corner and Morison got in front of Anthony Gardner to plant a header past Matt Duke.
Hull almost hit back immediately but home goalkeeper David Forde was equal to Richard Garcia's free-kick.
But they fell two behind just before the half-hour mark when Henry whipped in another dangerous cross and former Charlton striker Lisbie stole in to nod his first goal for the Lions.
Pearson had seen enough and hauled off Nolberto Solano for defender Paul McShane with 10 minutes of the first half remaining.
The move failed to stop the rot and Morison almost pounced on a mistake by Kamil Zayatte at the start of the second half, only to shoot high and wide.
But the striker, called up by Wales earlier this week, did not have to wait long to double his tally.
In a carbon copy of his first goal, Morison again beat Gardner to Henry's corner at the far post and looped his header past Duke and into the net.
With Hull in complete disarray, Trotter popped up to bundle home number four on the hour mark courtesy of another fine cross from the lively Henry.
The visitors went in search of a consolation but Forde ensured he kept a clean sheet with fine saves from Robert Koren, on his debut, and Andy Dawson.
But the Tigers had been well and truly mauled by the Lions, who could even have had a fifth when Darren Carter headed just over shortly before the final whistle.