Coventry, who are still not mathematically safe from relegation from the Championship, took the lead through King in the early stages on Saturday, only for Andros Townsend to drill home an equaliser in first-half injury time.
Millwall substitute Neil Harris was on the pitch for less than two minutes before he saw red for an off-the-ball incident with Aron Gunnarsson.
And King made the most of the Sky Blues' man advantage with his 12th goal of the season.
The result leaves the Lions four points off sixth-placed Leeds.
Coventry caretaker boss Andy Thorn made two changes from the side which claimed a 3-0 win at Portsmouth last time out, with Jordan Clarke and Carl Baker coming in for Nathan Cameron and Gary McSheffrey.
Millwall were without top scorer Steve Morison after he was sent off in the dying stages of the midweek draw with Bristol City. Jimmy Abdou, Darren Purse and Scott Barron were handed starting spots.
The Lions started brightly but gifted Coventry the lead after just seven minutes. A square pass from Purse was intercepted by King and he took the ball around goalkeeper David Forde before slotting home.
The visitors' response came from James Henry, but the midfielder's 20-yard drive was well held by Keiren Westwood.
Gunnarsson saw a shot blocked by Millwall defender Darren Ward, while at the other end Josh McQuoid failed to trouble Westwood with a mis-kick from 12 yards.
The chances continued to flow, with Forde doing well to block a shot from David Bell and Henry again missing by inches with a fizzing drive from just outside the area in the 36th minute.
An inswinging corner from Townsend caused problems for Westwood shortly afterwards, but the keeper managed to punch clear.
Millwall equalised on the stroke of half-time. Henry broke brilliantly from midfield and played the ball to Townsend, who advanced and slammed a low shot into the bottom corner.
Harris came on for Abdou at half-time but was on the pitch for less than two minutes. The veteran striker tangled with Gunnarsson off the ball and was shown a straight red card.
Coventry had the impetus, and King forced a superb save from Forde with a fierce drive from 18 yards in the 51st minute.
The Sky Blues lost Gunnarsson to injury moments later, with Michael McIndoe coming on. But it did not disrupt City too much as Baker brought the best out of Forde with a 25-yard piledriver.
Lukas Jutkiewicz had been anonymous for Coventry and was replaced by Clive Platt with 25 minutes left.
But it was Millwall who were next to attack, with the lively Townsend trying his luck from distance.
Thorn's men snatched the points with six minutes remaining when Richard Keogh's cross picked out King who had made a brilliant run, and the in-form striker coolly converted from six yards.