Vinales and Quartararo were over three tenths ahead of Honda’s Marc Marquez, who had been leading for most of the session before being later passed by the Yamahas.
Marquez rode in the tire tracks of Vinales for the opening minutes of the session and set a time of 1m33.171s, just two hundredths shy of Quartararo’s FP1 best.
The Championship leader had been running on a new soft tire and held an advantage of almost half a second over nearest rivals Vinales until those behind him fitted fresh rubber for the final heats of FP2.
First Valentino Rossi closed to within three tenths of Marquez before the other works Yamaha from Vinales registered the first attempt of the weekend under 1m33s.
That attempt of 1m32.775s was two tenths quicker than Quartararo’s first push lap on the soft rear tire and although the French rookie improved again at the checkered flag he was 0.057s shy of toppling Vinales.
With the top three made up of the same riders as in the morning session, Rossi was best in fourth, albeit seven tenths off pace.
Quartararo’s Petronas Yamaha teammate Franco Morbidelli made it into the top five on four Yamahas, while Pol Espargaro led KTM’s charge in sixth place.
The two factory Ducati’s of Danilo Petrucci and Andrea Dovizioso finished seventh and eighth, ahead of Suzuki’s Alex Rins and LCR Honda’s Cal Crutchlow.
However, Rins and Crutchlow are currently on course to miss out on automatic places in Q2, while Aleix Espargaro (Aprilia) and Michele Pirro (Ducati) instead finish in the top 10 of the combined standings on their FP1 laps.
Marquez’s Honda team-mate Jorge Lorenzo put in an improved performance compared to the morning session but remains in 17th place – 1.6 seconds separating the top 21.