The Premier League's Golden Boot holder had already guaranteed another match ball by the 40-minute mark as Pep Guardiola's men threatened to run away with the tie, although Jordan Clark gave Rob Edwards's side a glimmer of hope with a sensational effort before the break.
An outrageous Luton comeback was no longer fanciful when Clark netted his second of the night early in the second period, only for the uncontrollable Haaland to complete a five-star individual display before Mateo Kovacic briefly stole the spotlight too.
While still naming a strong XI, Guardiola offered opportunities to the likes of Jack Grealish, Matheus Nunes and Stefan Ortega at Kenilworth Road, but it was two of the usual suspects who linked up for the Citizens' opener with just four minutes gone.
Nunes was heavily involved in the build-up, flicking a cute pass through a charging De Bruyne in the left-hand side of the box, and Haaland arrived to guide the Belgian's cutback into the side of the net.
Luton's response to going behind was a positive one, though, and Carlton Morris would seemingly test Ortega from close range just three minutes after Haaland's opener, but Nathan Ake was on hand to make a terrific block.
The Hatters' brief period of promise soon petered out, though, and another combination from City's deadly duo ended with the net rippling for the second time in the 18th minute, as Haaland firstly took down a long pass from Ederson and laid the ball off to De Bruyne.
The Norwegian immediately sped away behind the Luton backline, latched onto an inch-perfect through ball from De Bruyne and fired through the legs of Tim Krul to put the holders in cruise control.
Only the legs of Krul denied Haaland a 25-minute hat-trick as the Scandinavian sensation got in behind the Hatters' defence once again, and the Dutchman bailed out his teammates again on the half-hour mark, producing a double save from a De Bruyne volley and Haaland follow-up.
As the first half entered its closing stages, both coaches were forced into unplanned alterations, as a miffed Grealish had to be replaced by Jeremy Doku, while injured Luton defender Amari'i Bell came off 18-year-old Joe Johnson.
The break in play did not harm City's momentum, though, and both Haaland and De Bruyne completed their respective hat-tricks of goals and assists in the 40th minute, where the Belgium international slipped his marksman through with another sublime pass, and Haaland did the rest with a slick chip above Krul's shoulder.
The Luton stopper appealed vehemently for offside, but his pleas fell on deaf ears as Haaland and De Bruyne terrorised the Hatters defence again, although none of the Norwegian's three efforts would prove to be the best goal of the half.
Indeed, a rare Luton attack in the 45th minute saw Ross Barkley tee up Clark, who shifted the ball onto his right foot 25 yards from goal and curled home an astonishing strike into the top corner, which left Ortega rooted to the spot.
After Krul stopped Nunes from restoring City's three-goal lead four minutes into the second half, a resurgent Luton gave their fans even more reason to believe in the 52nd minute, when the lively Barkley chipped a deft ball in behind the visitors' backline for Clark, who lashed a half-volley into the roof of the net for his second of the night.
While the Barkley-Clark combination presented the Hatters with unforeseen hope, the irrepressible Haaland-De Bruyne union extinguished such hope just three minutes later, as Kyle Walker released the latter down the right and witnessed De Bruyne square for Haaland to tap home his fourth of the night.
Another three minutes passed before the scintillating Scandinavian erased any seeds of doubt with an unbelievable fifth of the game in the 58th minute - albeit one set up rather than Bernardo Silva rather than De Bruyne - as his ferocious strike deflected into the Luton net via the body of Krul.
The battered and bruised hosts refused to give up the ghost, though, and Ortega was forced into a brilliant pair of stops in the 65th minute, coming out to meet Morris before tipping Barkley's curler around the post with his fingertips.
Guardiola's troops soon attacked the end where their jubilant fans were stood again, and Luton were officially hit for six in the 72nd minute, but rather than a double hat-trick for Haaland, it was Kovacic who rifled a 20-yard piledriver past Krul, who flapped at thin air and arguably should have done better.
Haaland would not end the night with a spellbinding six of his own as Guardiola rang the changes in the dying embers, but the 23-year-old departed having equalled a 54-year-old record set by George Best, the last player to score at least five goals in an FA Cup game for a top-flight side in 1970.
Man City now have the small matter of a Premier League Manchester derby with Manchester United on the agenda for Sunday, one day after Luton host Aston Villa in a Saturday evening showdown.