Andy Frampton and Chris Hackett had put the Lions in control at half-time in Tuesday’s League One clash at the New Den but Jermaine Easter netted twice to level before Morison’s late heroics.
Kenny Jackett’s men had taken the lead on 11 minutes when Marc Laird was allowed to swing in a left-footed cross into the penalty area and Frampton headed into the bottom corner from 10 yards.
And the Lions doubled their lead after 20 minutes, Hackett slotting home after keeper Wily Gueret had parried Danny Schofield’s effort.
But Easter kicked off the Dons fightback in fine style straight after the restart – latching onto a Martin Devaney through ball and smashing past keeper David Forde.
And with the Lions defence backing off at the opposite end, Easter netted a 79th-minute equaliser with a stunning 25-yard effort.
But Morison was to have the last word for Millwall, shrugging off the attentions of defender David McCracken and firing underneath Gueret.