Full-time from The Den
Morison was on hand to fire The Lions ahead after just five minutes and added his second, a superb volley, to put Neil Harris' charges in a commanding early lead.
But struggling Doncaster gave it a real go, and if they had shown a little more composure in front of goal, could have come away with at least a point after piling on the pressure in the second-half.
Doncaster boss Darren Ferguson had spoken before the game about the need for his team to come out and impose themselves on the game, but those words fell on deaf ears as his side committed defensive suicide twice in the opening eight minutes to hand The Lions a dream start.
There were just four minutes on the clock when a mix-up between keeper Thorsten Stuckmann and his defence enabled Lee Gregory to nip in and slip the ball through to Morison, whose effort flew over the bar.
However Donny failed to learn from that let-off and within 60 seconds yet another wayward pass at the back was again picked up, this time by Morison and the striker's shot took a deflection and looped over the keeper's head into the back of the net.
If Millwall's opening goal had a sprinkling of luck, their second was of the highest order. A move practiced on the training ground was executed to perfection on the pitch after eight minutes. Shane Ferguson whipped over a delightful free-kick from the left, picked out Morison on the right and he hit a stinging first-time volley that arrowed into the bottom corner of the net.
Doncaster responded to this early double blow and enjoyed a decent spell of pressure with Andy Butler wastefully heading over from eight yards from a Nathan Tyson cross and then Tyson somehow contriving to slice the ball wide of the target from five yards.
Gregory was a whisker away from increasing Millwall's tally on 25 minutes when he was played in by Aiden O'Brien following a barnstorming run by the young Irishman down the left flank. Gregory controlled the ball but saw his shot blocked by Stuckmann at the back post.
Morison twice squandered great opportunities to grab a hat-trick, turning Gregory's pinpoint cross from the right narrowly wide of a gaping net on 28 minutes and then powering a header over the bar from eight yards five minutes later following a neat move carved out down the left by Joe Martin and Ferguson.
Coppinger was a whisker away from connecting with Harry Middleton's super flighted through ball 10 minutes before the break as the visitors offered a timely reminder that they were far from finished as far as this game was concerned.
But The Lions finished the opening half in the ascendency and O'Brien was unlucky not to get on the score sheet. Gregory was again the provider, using good strength and control before laying the ball into O'Brien's path. Unfortunately the latter scuffed his shot and the ball bobbled a yard wide of the post.
Doncaster needed an instant response at the start of the second-half, and former Lions loanee Tyson could have got the visitors right back in it twice in the opening exchanges after the break. First, the striker was inches away from connecting with Aaron Taylor-Sinclair's inviting cross and then when Cedric Evina's shot was blocked, Taylor-Sinclair turned the ball into Tyson's path but he headed just wide.
At the other end Morison's search for his first ever hat-trick in a Millwall shirt continued as the striker was thwarted once more, this time Stuckmann flung himself low to his left to divert the striker's bullet header from Edwards' delightfully weighted cross.
Back came Donny, however, and Middleton's stinging 20-yarder slammed into the side netting as the visitors tried in vain to get a foothold in the match.
A 25-yard freekick from Harry Forrester took a wicked deflection and looked to be heading into the back of the net but thankfully dropped just wide for a corner as Harris' men breathed again.
The Den faithful really came into play now, and a rousing 'Miiiiiii' began to ring around the stadium as Lions fans tried to lift the team. It certainly worked and the players, with the fresh legs of Fred Onyedinma, Lee Martin and then Byron Webster all steadying the ship, did enough to see out the game and secure a third successive home League win.
Bookings: Thompson (80mins), Craig (80mins), Beevers (87mins), L.Martin (90+1min)
Scorer: Morison (5, 8mins)
Doncaster Rovers: Stuckmann, Lund (Williams, 77mins), Evina, McCullough, Butler, Wellens (Forrester, 53mins), Tyson, Taylor-Sinclair, Coppinger, Stewart (N'Guessan, 56mins), Middleton. Subs not used: Marosi, Gobern, Keegan, Whitehouse.
Ref: C. Breakspear
Att: 8,294 (away 195)