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.