Blues were on the back foot for the majority of the first half but they took their chance after the sorry hosts completely lost their discipline.
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 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.
Millwall manager Kenny Jackett made five changes to the side that drew at Dagenham & Redbridge in the FA Cup and it was one of those replacements who nearly put the hosts in front.
Hamer Bouazza picked out Dany N'Guessan at the near post but the striker could only head wide.
On-loan Tottenham striker Harry Kane then had his effort from Bouazza's corner cleared off the line by a perfectly positioned Jean Beausejour as the Lions continued to belie their lowly league position.
Despite being on the back foot for much of the early stages, Davies gave Blues an 18th-minute lead against the run of play.
The Blues defender burst in unmarked at the back post to head home Jordon Mutch's free-kick.
Millwall's defence had failed to pick up Davies' run but things went from bad to worse four minutes later as Lowry received a straight red card for an off-the-ball incident with Zigic.
Referee Jon Moss initially missed the incident but after consulting with his linesman, gave defender Lowry his marching orders.
Despite being reduced to 10 men, Millwall continued to dominate the contest until the interval and only a spectacular save from Blues goalkeeper Boaz Myhill denied Kane from finding the top corner with a 25-yard strike.
Blues started to gain the upper hand after the interval and their chances of coming away with all three points were enhanced even further when Millwall were reduced to nine men in the 57th minute when Dunne saw red after a tackle on Zigic from behind.
King took full advantage to double Blues' advantage two minutes later.
The striker collected the ball from Keith Fahey before turning and shooting past Millwall keeper David Forde.
Unsurprisingly, Blues controlled the tempo of the clash thereafter and a one-two between Burke and King ended with the former cutting into the box and firing into the top corner.
Substitute Rooney made it four with a thumping effort from the edge of the area after being teed up by Burke in the 81st minute.
The goalscorer then turned provider as his clever ball found King, who then rounded Forde before finishing for his second of the afternoon two minutes later, while Redmond hammered home a sixth from 12 yards in stoppage time.