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 Ducati 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 16th and only 15th on 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 GPs last month.
Source: Autosport