Reigning champion Marquez was aiming to become the first man to win 11 consecutive premier class races at the start of a campaign and beat Giacomo Agostini's record that has stood for nearly half a century.
However, the Repsol Honda man - who started on pole - was slow off the line in Brno and never really recovered as team-mate Pedrosa became the first man other than Marquez to win in MotoGP this season, holding off Jorge Lorenzo in a thrilling finish.
Marquez had to settle for fourth behind Valentino Rossi, meaning he finished off the podium for the first time in his MotoGP career when he has completed a race.
A sluggish Marquez start saw him slip to sixth by lap two as Lorenzo (Movistar Yamaha) and Andrea Iannone (Pramac Racing) led early on.
Pedrosa soon slipped past Iannone, while Marquez appeared to be en route to a customary surge through the field when the Spaniard moved up to fourth.
A keen battle with Iannone ensued and, with 18 laps remaining, the pair traded position on four occasions and touched twice, with Marquez eventually coming out on top before Rossi (Movistar Yamaha) also passed Iannone.
However, Marquez failed to show the sort of pace that has set him apart from the rest of the field this season and Rossi edged passed him with 10 laps to go.
At the front, Pedrosa - who sits second in the standings - was struggling to shake off a determined Lorenzo and he had a lead of just nine tenths of a second as the final lap began, but he was able to do just enough to pass the chequered flag first.
There was also a fierce battle between Iannone and Ducati's Andrea Dovizioso, the former eventually winning through.
Cal Crutchlow (Ducati) had re-joined the race after crashing early on before eventually retiring, while Eugene Laverty (Voltcom Suzuki) and Pol Espargaro (Monster Yamaha Tech3) were unharmed in separate crashes.
Despite not winning, Marquez still retains a 77-point lead over Pedrosa in the championship standings.