Dani Pedrosa was second ahead of Maverick Vinales as Spain completed a podium clean sweep.
Cal Crutchlow, who won the race last year to became Britain’s first MotoGP winner in 35 years, was fifth.
Crutchlow, 31, crashed at Turn 10 during Saturday’s practice session because of oil on the track in Brno and later said he was advised by MotoGP medical director Angel Charte to pull out of the qualifying session.
Marquez, the fourth leader of the championship this season, has 154 points – 14 more than Vinales.
The 24-year-old had started the day with a five-point lead over his compatriot.
Marquez has now won two races in a row after his success in Germany last month and three this season.