Stoke led after 10 minutes through Peter Crouch’s eighth goal of the season and they had the game under control until King levelled the tie in the 35th minute.
The home side took the lead six minutes into first-half injury-time as Cameron received a straight red card and Gestede stepped up to convert the penalty.
King scored again five minutes after the break to extend the Championship side’s lead and things went from bad to worse for the visitors as Marc Muniesa hobbled off with an injury chasing King, who raced through to complete his hat-trick with just 55 minutes on the clock.
The result meant an unhappy return to Ewood Park for Stoke boss Mark Hughes who managed Rovers for four years, leading them to an FA Cup semi-final in 2007.
Hughes named a strong team, while Rovers boss Gary Bowyer made eight changes – and was forced into another when Ben Marshall was replaced by Craig Conway after injuring his shoulder in the 10th minute.
Crouch then gave the visitors the lead when he tapped home from Victor Moses’ corner, but that seemed to revitalise Blackburn and they slowly grew into the game.
Blackburn’s first chance came through King after he intercepted a poor backpass by Muniesa, but Jack Butland made the save and Stoke could have taken the lead in the 30th minute after Simon Eastwood parried Moses’ shot, but Mame Biram Diouf could only sky the rebound over the bar from 12 yards.
Minutes later, King got his and Blackburn’s first. Conway’s corner was knocked on by Shane Duffy and the striker was there to head it home.
There were eight minutes of injury-time due to Marshall’s injury and Rovers used the opportunity to take the lead. Cameron pulled King back in the box and referee Anthony Taylor showed him a straight red card.
King’s strike partner, Gestede scored from the spot to give his side the lead. Butland went the wrong way and the ball went straight into the bottom right-hand corner.
The game was all but over five minutes into the second half as King extended Rover’s lead with another header that left Butland flailing.
The 23-year-old then completed his hat-trick in the 55th minute. Stoke were holding a high defensive line and the striker collected the ball about 10 yards from the halfway line, raced through the Stoke defence and his first-time shot beat Butland at his far post.
Marcus Olsson nearly extended Blackburn’s lead but Butland was alert to save his header and 10 minutes from time Diouf had an opprtunity to score a consolation but sent his shot high into the crowd.
Rovers will find out on Monday who they will face in the quarter-finals, while an embarrassed Stoke team must now concentrate on the league.