Shaun Williams put the hosts ahead from the penalty spot following a foul that earned Grant Hanley his marching orders, but Rovers' on-loan defender Michael Keane soon headed his side level.
Simeon Jackson thought he had won it for the hosts, netting Millwall's second penalty two minutes from time, but King struck in injury time to deny them a second win in 13 games.
The home side started the brighter of the two and were nearly ahead in the first five minutes when Scott McDonald met Ryan Fredericks' cross, only to see his headed effort palmed over by Paul Robinson.
From the resulting corner Steve Morison had a chance to add to his seven goals this season but saw a tame effort saved - with claims he was being held back in the area were waved away by referee Nigel Miller.
Millwall had David Forde to thank for keeping the tie level after just seven minutes when the Irish stopper kept out Luke Varney's lofted effort after he was set free by David Dunn.
Though the Lions looked shaky in defence, they attacked with vigour and went agonisingly close to going in front in the 15th minute when Owen Garvan's free kick evaded those in the box and crashed off Robinson's post.
Millwall continued to test the Rovers defence, with McDonald seeing his low drive batted away by Robinson in the 37th minute after he cut in off the left flank, but the first half ended goalless.
Blackburn emerged the livelier after the break but were a man and a goal down in the 55th minute when Hanley was sent off for bringing down Morison as the striker ran in on goal, with Williams calmly sending Robinson the wrong way from the resulting spot-kick.
Gary Bowyer's side must have feared the worst but Millwall have conceded a division high of 67 goals this season and it was 68 just minutes after Williams' opener, when Keane leapt highest from Craig Conway's corner to head in the equaliser.
Despite being a man down, it was Bowyer's men pushing for the winner and Keane came close to scoring his second goal of the game when his headed effort was tipped Forde.
With just three minutes of normal time remaining, Millwall were awarded their second penalty of the match after substitute Jackson was pulled to ground by Keane and it was Jackson who stepped forward to arrow the ball into the bottom left-hand corner.
The referee signalled five additional minutes and two minutes into stoppage time King denied Millwall a much-needed three points when he scrambled Conway's cross home.