Rovers led 2-0, 3-2 and finally emerged exhausted but triumphant as 4-3 victors at Ewood Park, while the Magpies saw the end of their unbeaten run this season.
Ruben Rochina and Yakubu had apparently sent Blackburn on their way to a comfortable win, only for Danny Guthrie and Yohan Cabaye to hit stunning injury time strikes to send the game into extra-time.
Morten Gamst Pedersen's free-kick made it 3-2, Peter Lovenkrands equalised again from the spot and then came Givet's last-gasp heroics.
Rovers will argue it was about time the dice rolled for them - because they had appeared to be stacked against Steve Kean's side at kick-off.
Newcastle arrived with the best defensive record in the top flight, and with 4,500 travelling fans making up almost half the 10,682-strong crowd.
For most of the match and deep into injury time Blackburn had played like the unbeaten team, and Newcastle like the bottom club, before it all turned around in those two crazy minutes.
Blackburn started brightly and Junior Hoilett's extraordinary pace took him past two players, but Davide Santon - making his full debut - did well to block Ruben Rochina after he had seized on the cut-back.
Newcastle did not heed the warning however and the 20-year-old Spaniard was not to be denied when given a second opening in the fifth minute.
The chance was created on the left again, Martin Olsson playing a one-two with Hoilett before sprinting down the flank and crossing low for Rochina to sweep home from 12 yards out.
The stage had been set for an open contest and so it continued as Demba Ba fired against the post for the visitors after being put clean through by Danny Guthrie, then David Goodwillie brought a smart save out of the Magpies keeper Tim Krul.
Newcastle's discomfort in defence continued however and Fabricio Coloccini was extremely lucky to only receive a caution when he caught Yakubu high with his foot apparently raised.
Yakubu nearly made the Magpies pay again just before the break but Krul turned aside his curling shot.
The second half began with Hoilett drifting a 20-yard free-kick into Krul's arms, before the travelling fans exploded into indignation after referee Robert Madley refused to award a penalty when Sylvain Marveaux blasted the ball against Olsson's arm.
Yakubu was next to threaten but in the end his effort at Krul was feeble, before two hugely controversial incidents ended up with Blackburn extending their lead.
First Ba tangled with Chris Samba in the Blackburn box but Madley was unmoved, although it looked as though the Newcastle player had a good case.
The ball was swept down the other end to Rochina who beat the offside trap but lost control as Krul approached and then threw himself over the keeper's leg - and bizarrely this time the referee did point to the spot.
Yakubu made no mistake with the penalty - leaving the visiting fans chanting '2-0 to the referee' in frustration.
With Blackburn believing the game was in the bag, Guthrie hammered in a stunning shot from 30 yards.
That strike came in the third minute of injury time, and there were two agonising minutes for Rovers to endure.
There was one more chance for Newcastle - and that was enough. Samba fouled Coloccini 25 yards out and Cabaye curled a delightful free-kick into the top corner to send the tie into extra-time.
Pedersen had sent one howitzer of a free-kick wide but the Norwegian found the target soon afterwards, his drive skimming off the wall and low past Krul.
There still looked to be goals in this game and so it proved when Grant Hanley was penalised for a tug on Lovenkrands and the Dane tucked home the penalty to make it three apiece.
Still Rovers refused to give up the ghost and in the dying seconds Pedersen floated in a free-kick, Samba headed across goal and Gael Givet stooped to conquer at the far-post.
Cue a massive pile-on of Rovers players - this was some match and Blackburn had, finally, deserved it.