The in-form Lions had won four of their last five matches to surge towards the top six and raise hopes of back-to-back promotions in south London.
But they dropped two points against a City side in no mood to roll over despite treading water in mid-table.
And a straight red card for Morison, for a stoppage-time lunge on Jamal Campbell-Ryce, could be even more damaging with their 17-goal top scorer now set to miss most of the run-in through suspension.
Defeat for Leeds meant the Lions actually clawed a point closer to the sixth-placed Yorkshiremen.
But the visitors could have snatched all three points had Nicky Maynard not fluffed a glorious late chance.
City were also the more threatening early on through the lively pair of Maynard and Albert Adomah, and then defended resolutely as Millwall’s attacks became ever more desperate.
Maynard headed Adomah’s cross wide in the opening stages and former Lion Marvin Elliott might have done better with a free header from Jordan Spence’s centre.
David Forde should have been tested when the ball fell to Brett Pitman outside the area with the Lions goalkeeper well off his line, but the striker’s limp attempt at a lob landed straight in his arms.
Not that Millwall were faring any better at the other end.
Morison and Paul Robinson both headed tamely wide while Josh McQuoid fired across goal.
They almost embarrassed David James when Andros Townsend’s shot took a wild deflection and looped high into the air before dropping just under the City crossbar.
The England World Cup goalkeeper’s ungainly flap at the ball fell to Morison, but the angle was too tight and James was able to block his effort.
Millwall poured forward in the second half with Tamika Mkandawire blazing over from the edge of the area, Townsend firing straight at James and James Henry curling wide.
City remained a threat on the break, though, and just before the hour mark Martyn Woolford was only denied from 20 yards by a superb diving save from Forde.
Lions’ hearts were in their mouths when Maynard burst through with four minutes left and the offside flag stayed down, but the striker stumbled as he was bearing down on goal and the grateful Forde was able to save.
But the drama was not over and in stoppage-time Morison’s pointless lunge at Campbell-Ryce, near the touchline on the halfway line, earned him a straight red card.