The Briton shattered Bute's unbeaten record and took his IBF Super Middleweight belt with a performance of unrelenting power at a euphoric Capital FM Arena.
Confusion momentarily reigned when referee Earl Brown separated the fighters as Froch piled into his opponent.
Froch's promoter Eddie Hearn leapt into the ring and lifted his fighter skywards - however, Brown had not stopped the fight and was merely giving Bute a count.
Fortunately, controversy was averted when Bute's corner threw in the towel to spare their man any more punishment.
The highly-rated Romanian-Canadian came in boasting a 30-0 record, and the fight was a huge risk for the 34-year-old Froch, who lost his WBC Super Middleweight belt to Andre Ward in December and revealed he would have retired had Bute beaten him.
Froch leapt out of the blocks with an aggressive first round in which both fighters landed significant blows; the East Midlander's approach bordered on recklessness and he was admonished by his corner after walking into a couple of big left hands.
Yet Bute, who has fought all but five of his pro fights in his Quebec base, looked ill-at-ease and never connected with his jab.
Sensing he had his opponent rattled, Froch unleashed a flurry of big shots to the head and body in round three as Bute rocked back on the ropes.
The Romanian somehow held on until the bell, and showed greater initiative in the fourth with a smart uppercut and some solid body shots.
But Froch soon had his opponent reeling on the ropes again - looking like a recreation of the early round of the Rumble in the Jungle, when George Foreman laid mercilessly into Muhammad Ali.
There was no Ali-like recovery from Bute, though, and as Froch continued to pummel his adversary in round five, referee Brown stepped in.
The finish brought a delirious reaction from the home crowd on one of the great British boxing nights, one that cements Froch's reputation as one of the most resilient fighters these isles have produced.
"I came here more determined than I've ever been before," Froch told Sky Sports. "I've been guilty of switching off in the past but tonight I've been very focused."
Eurosport-Yahoo! unofficial scorecard
Round 1: Froch 9-10 Bute
Round 2: Froch 10-9 Bute
Round 3: Froch 10-9 Bute
Round 4: Froch 10-9 Bute
Round 5: Fight stopped