The Italian, who earlier smashed the lap record in qualifying, took the chequered flag 2.545 seconds ahead of LCR Honda's Alex Rins (27).
Spaniard Jorge Martin (25) finished third, after starting in 12th place and battling illness, for the non-factory Pramac Ducati team.
The 12 points for the win left Bagnaia one point adrift of VR46 Ducati's Bezzecchi, who finished sixth, with the main race to come on Sunday.
"I preferred this sprint race to the one in Argentina, that I was more in trouble," said Bagnaia, who started on the front row two weeks ago but finished only sixth.
"I started well, I just tried to push and do my pace and it was enough to open a gap. The conditions today were quite tricky for the hot temperature. On the braking it was very, very slippery."
Bagnaia battled Rins early on, with the Honda rider taking the lead into turn one and trading places before the Italian pulled away.
Rins then ceded second place to Aprilia's Aleix Espargaro (33) and nearly lost third to Yamaha's attacking French rider Fabio Quartararo (23), the 2021 world champion.
Quartararo's challenge faded and he crashed at turn one on lap five, sliding off but managing to remount and get back in the race to finish 19th.
Gresini Ducati rider Alex Marquez (26), brother of the injured and absent six-time MotoGP champion Marc (30), fell a lap later at turn 12 while battling for a top five place.
Ducati's tester Michele Pirro (36), replacing the injured Enea Bastianini (25), was another faller.
Martin meanwhile passed Espargaro for third and held off a challenge at the penultimate corner of the last lap.
"I gave my 100%. I couldn't breathe, after three or four laps I had no lungs any more. It was really difficult to keep the pace," said Martin.
"At the end I just tried to keep calm. I knew Aleix was faster.
"We need a good dinner tonight to get the power for tomorrow."
