The prolific Norwegian followed up his five-goal haul against RB Leipzig on Tuesday with his sixth treble of the season as City ruthlessly put the Clarets to the sword at the Etihad Stadium.
World Cup winner Julian Alvarez celebrated his new contract with a double and 20-year-old Cole Palmer also got on the scoresheet as former City captain Kompany endured a miserable return to his old ground.
Much of the pre-match build-up had been about Kompany, who won 10 major trophies in a glittering playing career with City and has a statue outside the stadium.
Naturally, he was given a great reception by the home fans but his former team showed him no niceties and, by the final whistle, the headlines were once again about Haaland.
The 22-year-old has now scored a remarkable 42 goals in 37 appearances in all competitions this term.
Burnley, the runaway Championship leaders, started confidently and Stefan Ortega was almost caught out as he was rushed into a pass and gifted the ball to Ian Maatsen.
Rico Lewis raced back to avert danger and Ortega made amends somewhat a few moments later when he pushed away a long-range effort from Nathan Tella.
Yet as uneasy as City looked at times in their own half, they were confident and slick at the other end.
Burnley had an escape when Haaland misdirected a header from a Phil Foden cross and it took a good tackle from Jordan Beyer to prevent Alvarez shooting.
Such was City's quality they could punish Burnley at any moment and a quickfire Haaland double just after the half hour put the game beyond the Clarets.
Haaland was fed on the edge of the area by Alvarez and, although Bailey Peacock-Farrell rushed out, he instinctively poked the ball beyond the keeper.
It was a smart finish but his next just moments later was even sweeter.
This time Foden was the provider after a charge down the left. His low ball into the area arced invitingly for Haaland and he lifted it neatly over Peacock-Farrell.
Burnley tried to respond and Maatsen forced a good save from Ortega just before the interval but City and Haaland were in no mood to relent.
Peacock-Farrell blocked a Riyad Mahrez volley and then beat away a Haaland strike but he could not stem the tide for long.
Haaland completed his treble just before the hour when, as usual, he was in the right place at the right time to pounce on a rebound after Foden hit the post.
He gave Peacock-Farrell no chance as he rifled home and the score quickly became 4-0 as Kevin De Bruyne burst into the area and squared for Alvarez to tap home.
As he was in midweek, Haaland was taken off in the 63rd minute. That meant his contribution for the week totalled eight goals from just 126 minutes of action.
There was still no respite for Burnley as Foden's cross was pushed into the path of Palmer and the substitute turned in.
The sixth came soon after as Alvarez raced onto a De Bruyne through ball and turned inside Ameen Al-Dakhil to thump home.
City coasted through the final few minutes and can now look forward to another trip to Wembley next month.