Phil Foden, John Stones and Matheus Nunes also struck as City broke a Manchester United record for the most consecutive games unbeaten in the competition in a one-sided contest at the Etihad Stadium.
Haaland's double took his goal tally to a remarkable 44 in 42 Champions League outings, his first being a gravitydefying backheel volley after Foden had opened the scoring.
He then claimed his 13th of the season with a smart finish after Stones had headed his third of the campaign, while a late Nunes penalty wrapped up the game.
Three of City's goals came in a blistering nine-minute spell in the second half as Pep Guardiola's side extended their unbeaten run in Europe's elite competition to a record 26 games.
That eclipsed the previous best of 25 set by rivals United from 2007-09, with City's only loss since the 2022 semi-finals coming via a penalty shoot-out after two draws against Real Madrid.
The victory took them to seven points after three games of the league phase, putting them on course for the next stage.
They did not need to hit top gear to see off the Czechs, and made light of the absence of Jack Grealish and Jeremy Doku, who became the latest additions to their injury list prior to the match.
City got off to a superb start as Foden put them ahead after just three minutes.
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