Morison should have had at least a couple more in the second half as the Cumbrians' lack of pace at the back was exploited by the dangerous Lions attack.
Carlisle started brightly enough, but Millwall soon hit their stride and went ahead in the 13th minute when Morison seized on Shaun Batt's headed flick to cleverly lob goalkeeper Adam Collin from the edge of the area.
Morison was inches away from a second goal in the 51st minute when he sprinted clear of the defence. The striker cut in from the left but somehow Collin got enough on the shot to send the ball spinning across the face of goal and out for a corner.
Again a lack of pace at the back was exposed in the 72nd minute when Morison broke away but failed to find the target with just the keeper to beat. However, he did find the target with 12 minutes remaining when Collin came to collect Danny Schofield's cross from the left but missed the ball entirely, leaving Morison with a simple finish at the far post.
Danny Livesey pulled one back when he headed home Matty Robson's corner, but with seconds left Schofield made it 3-1 to the Lions, tapping home Morison's cross from close range.