The Yamaha rider spent the nearly 45-minute practice session running a long lap loop ahead of the punishment he will deliver on Sunday.
His first attempt, a 2m00.794s, put him in third place, behind the Aprilias of Maverick Vinales and Aleix Espargaro.
He fell on the timesheet while others improved as he worked on improving his time around the long lap loop.
His fifth attempt brought him back into the top three, a 1m59.933s, before a last-minute attempt took him to the top of the timesheet as the only driver to set a sub-1m59s time with a 1m58.946s.
Suzuki’s Joan Mir finished second, less than 0.1s behind the championship leader, with Vinales in third with 1m59.123s.
Miguel Oliveira led the times in the early part of the session, the KTM man clocking 2m00.863s in the opening laps.
Pramac Ducati rider Johann Zarco continued his fast run from FP1, setting a 2m01.219s to slot in behind Oliveira.
The yellow flags waved briefly as Darryn Binder spun in Turn 6, losing the rear of his RNF Yamaha.
Jorge Martin was next to make his way into the top two, a 2m00.873s fast to edge out teammate Zarco.
The Aprilia pair were next fastest, Vinales leading Espargaro with 2m00.484s, while Quartararo finished third.
Oliveira briefly took the lead next before VR46 rider Marco Bezzecchi, who took his maiden podium last time out in Assen with a second-place finish, pipped him by 2m00.204s.
After 10 minutes of the session, times began to drop, with Alex Rins next leading for Suzuki before the Aprilias returned to the top, despite Espargaro struggling at the rear at Copse.
Rins was fastest on his 10th tour, a 1m59.351s quick enough to put him on top, before Ducati’s Jack Miller split the Aprilias into third.
Shortly thereafter, Miller went down in Turn 7 prompting yellow flags as his factory bike recovered from the gravel at Stowe.
Rins improved even more a few laps later, pushing him 0.4s ahead of Espargaro at the top of the combined standings.
Teammate Mir finished second with 1m59.536s, before Espargaro also improved with 1m59.426s.
But the Suzuki man improved again in the following lap, 1m59.100s enough to lead until Quartararo’s last attempt.
Zarco finished fourth, with Espargaro and Oliveira fifth and sixth respectively.
Gresini Racing’s Enea Bastianini finished the session in eighth after testing a radical new rear aero package, also seen on Martin’s bike, while Miller and Bezzecchi rounded off the top 10.