Millwall made an impressive start to the match, and took the lead after just five minutes as Rovers keeper Thorsten Stuckmann misplaced a goal kick, before Morison latched on to the ball and finished past the German.
Morison doubled the Lions' lead three minutes later, as the former Norwich City man volleyed past Stuckmann from a Shane Ferguson free kick.
Doncaster responded well to the second goal, and almost pulled one back when Andy Butler headed over the bar from a Nathan Tyson cross, before the former Derby County striker blazed an effort over the bar from four yards.
The hosts could have added a third goal before the 30-minute mark as Lee Gregory forced a save from Stuckmann, before the forward found Morison with an inviting cross only for the veteran to spurn his hat-trick opportunity by firing wide.
Millwall nearly found the net again before half time, as O'Brien and Gregory exchanged passes, only for the former to drag an effort wide from six yards. body check tags ::