Till retrieved the loose ball and, at the second time of asking, found Darren Byfield who drilled a low shot beyond David Forde from 12 yards.
Forde held a speculative Byfield drive after 20 minutes, but then Millwall began to take charge.
Morison headed a Danny Schofield corner over the bar seven minutes before the interval and, on the stroke of half-time, Ashley Grimes wasted Millwall's best chance when he blazed over from 12 yards.
But Grimes made amends just before the hour when he laid on for Morison to finish emphatically from 18 yards.
And he sealed the points 15 minutes from time, this time latching on to Jason Price's pass to send a similarly rasping finish beyond the despairing Forde.