Jason Koumas tested Andy Marshall early on, but Millwall had the better of the first half with Barry Hayles a continual threat to Cardiff's goal.
Substitute Alan Lee gave the visitors some impetus, but Marshall was on hand to deny Jeff Whitley and Glenn Loovens.
The abrasive Morris saw yellow for dissent in the first half, and an injury time foul on Koumas led to red.
The draw stretched Cardiff's unbeaten run to seven games and Millwall's to four.
Cardiff boss Dave Jones:
"I have to admit I think that the game had 0-0 written all over it from about 15 minutes into the game and I think it would have been unfair had either side come away from this game with three points.
"But I feel that had we got at them a little bit more we would have come away with all three points."
Millwall: Marshall, Vincent, Phillips (Lawrence 45), Williams, Ifil, Livermore, Wright, Morris, Dunne, Hayles, Asaba.
Subs Not Used: Hutchison, Braniff, Simpson, Jones.
Sent Off: Morris (90).
Booked: Morris.
Cardiff: Alexander, Weston, Purse, Loovens, Barker, Koumas, Whitley, Ledley, Cooper, Ricketts (Lee 72), Jerome.
Subs Not Used: Cox, Ardley, Parry, Margetson.
Booked: Weston, Whitley, Ricketts.
Att: 9,254
Ref: A D'Urso (Essex).