Team mate and compatriot Dani Pedrosa was second with Yamaha's world champion Jorge Lorenzo, the early leader, making it three Spaniards on the podium with third place after a three-way battle in Brno.
Italian Valentino Rossi, the last rider to win four successive MotoGP races in 2008, was fourth for Yamaha.
Marquez now has 213 points to Pedrosa's 187 with Lorenzo on 169.
"I enjoyed the battle," said Marquez. "It is the first time I have had a fight like this in MotoGP. In the beginning Jorge pushed quite a bit and made a big gap, but in the end I was a little bit stronger."
Tech3 Yamaha rider Cal Crutchlow, who started on pole position for the second time this season, again failed in his bid to become the first British winner in the top category since Barry Sheene in 1981.
Crutchlow dropped back to fourth at the start and then crashed on lap eight before returning at the back and finishing 17th.
"I was trying to push to get back to the front guys but I made a mistake," he told the BBC.
In the Moto2 class, Finland's Mika Kallio took his first victory in the category while Britain's Scott Redding saw his overall lead over Spain's Pol Espargaro trimmed to 21 with seven rounds remaining.
The next race is the British Grand Prix at Silverstone on September 1.
(Reporting by Alan Baldwin in Spa-Francorchamps; Editing by John Mehaffey)
