The reigning world champion set a 1m45.436s to top the timesheets in the final five minutes of the session, having entered FP2 in 16th overall.
Having been running outside the top 10 early on, factory Ducati rider Bagnaia had a brief off at San Donato, heading into the gravel.
He continued before improving to third with a 1m46.944s, chipping off lap time as the session continued before both he and Bezzecchi demoted Alex Rins from the top spot.
VR46 rider Bezzecchi, who sits just one point behind Bagnaia in the standings, was second-quickest just 0.063s off his fellow Italian, with LCR Honda rider Rins in third.
Quartararo’s struggles continued on the factory Yamaha as he finished the session 15th in the combined timings, failing to improve on the time which saw him finish second in FP1 this morning.
It was the third race in a row which saw the Frenchman fail to head straight into Q2 after the Spanish and French Grands Prix last month.
Miguel Oliveira, returning from a dislocated shoulder which he suffered in Jerez, took an early lead on his RNF Aprilia, with a 1m47.103s to lead from Pramac’s Johann Zarco and Marc Marquez.
Gresini rider Alex Marquez, who led FP1, was next to go quickest with a 1m46.723s, before Zarco once again secured the top spot while Bagnaia slotted into third.
Jorge Martin was next to lead, bettering his team-mate’s time with a 1m46.303s, with Rins taking second place despite having a near-miss with Gresini’s Fabio Di Giannantonio.
Bezzecchi improved to a 1m46.218s before the yellow flags were waved in sector four as Marc Marquez slid off his Honda at Turn 15 with 10 minutes remaining, cancelling Ducati rider Enea Bastianini’s lap.
Heading into the final stages, the times began to tumble, with Brad Binder leading before the KTM rider’s time was bettered first by Martin, then Bezzecchi.
Marc Marquez took the lead with a 1m45.691s before Rins regained the top spot and the order reshuffled, with red sectors across the board as the field fought for the 10 Q2 spots.
The yellow flags were again waved as Di Giannantonio headed into the gravel at Turn 1, scuppering Quartararo’s final lap, which was cancelled, leaving the Frenchman heading again into Q1.
Binder finished third, ahead of Martin and a returning Bastianini, who hopes to make his first race start since Portugal where he suffered a fractured shoulder blade.
Zarco finished seventh ahead of Marc Marquez and Aleix Espargaro, who made it inside the top 10 despite battling an ankle injury, returning to his garage during the session to ice the bruising.
Luca Marini, also suffering from injury with damage to his right trapezium bone after a crash during the French GP, rounded off the top 10.