The bottom-half battle had been rescheduled for Wednesday evening due to Tom Lockyer's distressing on-field collapse during December's clash, which was abandoned with the two sides level at 1-1.
Following a couple of moving pre-match tributes to the present Lockyer, who was featured on the pre-game programme cover and made his way around the stadium to a standing ovation, his Luton side got off to an incredible start as Tahith Chong, Chiedozie Ogbene and Ross Barkley gave the visitors a 3-0 first-half lead.
Rob Edwards's men would seemingly be clambering above the dreaded dotted line, but to the astonishment of the Vitality crowd, Bournemouth produced a breathtaking second-half turnaround through Dominic Solanke, Ilya Zabarnyi and a brace from Antoine Semenyo, becoming the first side in the Premier League to come back from three goals down to win after Wolverhampton Wanderers did so against Leicester City 20 years ago.
In the wake of his forgettable outing against Sheffield United, Bournemouth's top scorer Solanke saw the game's first real chance fall his way in the fourth minute, but his header from Semenyo's delivery flew harmlessly wide.
Just five minutes after Solanke fluffed his lines, Luton's Chong offered him a heading lesson with the Hatters' opening goal at the Vitality, finding himself totally unmarked inside the six-yard box and nodding in past a flat-footed Neto.
The Cherries' defending left a lot to be desired, although their response to going behind was a good one, as Luis Sinisterra tested the gloves of Thomas Kaminski in the 16th and 24th minutes.
Luton were otherwise quelling their hosts with relative ease, and during a rare period of possession, Edwards's men delivered a 31st-minute sucker-punch, as Chong split the Bournemouth defence open with a perfectly-weighted pass to Alfie Doughty, whose low ball to the back stick was tapped in by Ogbene.
Bournemouth continued to huff and puff, but the Luton walls were proving too sturdy to be blown down, and in the first minute of added time, the Hatters once again turned defence into attack to devastating effect.
Building up down the right this time, Issa Kabore slipped in Barkley - being kept onside by Lewis Cook as his teammates pushed up the field - and the regenerated Englishman rifled a ferocious finish into the roof of the net at Neto's near post.
After his below-par troops were booed off at the whistle, Iraola pulled no punches during the break, introducing Enes Unal and Marcus Tavernier for Alex Scott and Sinisterra, but it was their goalscoring talisman who reduced the arrears just five minutes after the restart.
As Bournemouth recycled a corner to a central position, Chris Mepham headed Tavernier's deflected shot into the mixer for Solanke, who produced an outrageous turn to evade Daiki Hashioka and Reece Burke before calmly lifting the ball over Kaminski.
Despite a hint of offside against Mepham, a VAR review confirmed Solanke's goal to set up a fascinating finale, in which Chong had the ball in the back of the net for a second time in the 54th minute only to be denied by the offside flag.
Solanke's 15th Premier League goal of the season would prove to be the catalyst for an unbelievable Bournemouth fightback, as the Cherries found their second in the 62nd minute, when Zabarnyi headed the ball over the line after a combination of Kaminski and Doughty kept out Unal's near-post effort from a Cook corner.
Doughty did his utmost to stop Zabarnyi's looping header from crossing the line, but his efforts were futile, and just two moments later, a barnstorming Bournemouth comeback was complete.
Facing up to Hashioka on the right, Semenyo was given licence to advance into the box and cut in on his left foot before beating Kaminski with a stunning low finish at his near post, thus wiping out Luton's seemingly unassailable three-goal lead.
Somehow back on level terms, Iraola's charges relentlessly searched for number four against a dumbstruck Luton, who would remarkably fall behind for the first time in the 83rd minute, when Unal slipped Semenyo through with a delightful pass inside, and the 24-year-old did the rest with a crisp finish into the far side of the net.
A couple of chances for number five came and went for Bournemouth - and more specifically Unal - in added time, but the Cherries had done enough to snatch the unlikeliest of victories from the jaws of defeat, as a crestfallen Luton rued their catastrophic second-half collapse.
As a result, there is no change to either side's standing in the Premier League table, as Luton remain 18th with a three-point gap to make up to Nottingham Forest, while Bournemouth reside in 13th but are only behind Fulham on goal difference.
Edwards's men will have another chance to rise to safety before the international break, hosting Forest in a crucial basement battle on Saturday, while the Cherries have over two weeks to recuperate from Wednesday's extravaganza before welcoming Everton to the South Coast on March 30.