The 23-year-old, on only his 14th appearance this season and with just one league goal to his name, terrorised a Potters defence which was severely hampered by the sending off of Geoff Cameron just before half-time.
Former Rovers boss Mark Hughes, a three-time FA Cup winner with Manchester United, could only watch as the ex-Red Devils youth team player sent his side crashing out of the competition and Rovers into the quarter-finals for the second time in three years.
King's poacher's finish cancelled out Peter Crouch's early goal before he won the penalty from which Rudy Gestede scored his 14th of the campaign when he was pulled back by Cameron.
The 23-year-old Norway international had caused the visitors problems with his blistering pace before the break but he enjoyed the extra space available against 10 men for 45 minutes and twice raced clear to score with virtually identical goals just 10 minutes into the second half.
King, who attracted some interest from struggling Barclays Premier League clubs in the January transfer window, is out of contract in the summer and if this performance cannot persuade manager Gary Bowyer to offer him a new deal then it will certainly have made someone else's mind up.
Despite beating another top-flight side Swansea at home in the last round, the priority for Rovers is to close the gap to the Sky Bet Championship play-off places so, with that in mind, manager Gary Bowyer made eight changes from the midweek win over Rotherham.
Hughes, by contrast, was targeting some silverware and his only alteration from the team which lost to Manchester City on Wednesday was a switch of goalkeepers with England international Jack Butland replacing established number one Asmir Begovic.
There was a sense that Rovers were missing an opportunity and that was reflected in the crowd of 13,934, although that would have been more had police not objected to Stoke having an extra allocation of 2,000 on safety grounds.
When Crouch, on target for the third successive match, smashed home a 10th-minute Victor Moses corner it appeared the script was being followed.
Marko Arnautovic and Mame Biram Diouf had chances to put the game bed inside half-an-hour but let Rovers off the hook and King, at the heart of every real threat, took full advantage.
He should have equalised midway through the half with only the goalkeeper to beat but his shot grazed the crossbar and he also guided a header wide before, after 36 minutes, he deflected Shane Duffy's powerful header past Butland from close range.
Having created a good chance for Gestede after stripping Philipp Wollscheid for speed, only for his team-mate to fluff his shot, King was fouled by Cameron in the eight minutes of stoppage time for three lengthy injury breaks.
The Stoke defender was shown a straight red card by referee Anthony Taylor and Gestede did not make a mistake with his second chance from the spot.
Rovers ensured there would be no turnaround of momentum in the second half as King - who had scored five goals in his previous 68 appearances - twice raced through to slot the ball past Butland in carbon-copy goals within five minutes of each other.
Stoke were deflated and dejected and home fans took great delight in taunting their former manager.
It all got a bit too much for some of the visiting supporters, some of whom became involved in a minor scuffle with stewards and police late in the game.
Hughes ordered his players to go acknowledge what was left of the travelling fans at the final whistle.
It looked more like an offer of an apology but that should not take anything away from another impressive cup performance from Blackburn.
Source : PA