Blues capitalised after the hosts completely lost their discipline at The Den on Saturday afternoon.
Curtis Davies gave Blues an 18th-minute lead against the run of play before the Lions' chances were hampered when Shane Lowry was sent off for an off-the-ball incident with Nikola Zigic.
Zigic was at the centre of the action again as he was felled by Alan Dunne's tackle from behind, with the defender also given a straight red card.
From there on, Blues ran riot as strikes from Marlon King and then Chris Burke ensured the three points.
Further efforts from Adam Rooney, another from King and Nathan Redmond ensured Blues extended their unbeaten run to six matches in some style.
"After having not started the game too well, we probably went in front against the run of play, but we were then able to capitalise on the circumstances and the space we were afforded," the Blues boss told Sky Sports after the game.
"You have still got to put the ball in the back of the net, though, and that is something that we have found a little bit more difficult away from home, so certainly it is a good feeling to get the goals.
"You are up against initially 10 men with a crowd that is going to push their team on and contest every decision, so it is never easy, but, of course, it is easier when 10 becomes nine.
"But as I say you have still got to break a team down, get into the spaces and take your chances - we were clinical enough which was great."