Rins fastest as Quartararo eighth in Qatar MotoGP practice
Suzuki's Rins was 0.035 seconds faster at the Losail circuit than six-time world champion Marc Marquez, whose past two seasons have been derailed by injuries.
Joan Mir, winner of the 2020 title, posted the third best time while Frenchman Quartararo could only manage eighth on his Yamaha.
Last year's championship runner-up Francesco Bagnaia moved up to 10th in the day's second session after crashing during the first run, when South Africa Brad Binder of KTM surprisingly set the pace.
Two further sessions will be held on Saturday, the first in the afternoon heat, before qualifying begins at 1500 GMT, the same time as Sunday's race.
During practice several riders wore helmets with stickers reading "Give Peace a Chance" in response to the Russian invasion of Ukraine.
Riders on Thursday posed for the traditional start-of-season grid photo behind a banner proclaiming "United for Peace".
The Qatar MotoGP is the first of a record 21 races this season, which ends on November 6 in Valencia.
It will be the first this century without the recently retired Valentino Rossi, who announced Friday the birth of his first child, a daughter named Giulietta.
Combined practice times:
1. Alex Rins (ESP/Suzuki) 1:53.432, 2. Marc Marquez (ESP/Honda) at 0.035sec, 3. Joan Mir (ESP/Suzuki) 0.147, 4. Jorge Martin (ESP/Ducati-Pramac) 0.220, 5. Franco Morbidelli (ITA/Yamaha) 0.413, 6. Jack Miller (AUS/Ducati) 0.438, 7. Aleix Espargaro (ESP/Aprilia) 0.454, 8. Fabio Quartararo (FRA/Yamaha) 0.474, 9. Pol Espargaro (ESP/Honda) 0.531, 10. Francesco Bagnaia (ITA/Ducati) 0.539