Marquez, unbeaten at the Sachsenring in various classes of grand prix racing since 2009, established a big lead five minutes into the session and better his laptime a few more times.
He ended his run with 1m21.464s, with only Alex Rins also able to break the 1m22s barrier with a 1m21.967s
The top two remained unchanged until the final two minutes of the session when Yamaha duo Valentino Rossi and Quartararo moved in front of Rins.
The Frenchman was then able to edge Marquez out by 0.074s as well, and topped FP1 with a 1m21.390s, before ending his session with an off-track excursion at Turn 8. Marquez was second, with Rossi beating Rins by 0.003s for third.
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Maverick Vinales was only the third Yamaha in fifth, over eight tenths off the pace, with Andrea Dovizioso leading Ducati’s efforts in sixth.
Pramac Ducati’s Jack Miller took seventh ahead of the Aprilia of Andrea Iannone and the injured LCR duo Takaaki Nakagami and Cal Crutchlow.
Pol Espargaro was the top KTM in 11th, just over one second off the pace.
Newly re-signed Ducati works rider Danilo Petrucci was 15th, while Stefan Bradl, Jorge Lorenzo’s replacement at Repsol Honda, kicked off his home round in 17th.
Francesco Bagnaia was the only rider to crash, the Pramac rider falling at Turn 8.