Bagnaia held off Quartararo in a pulsating late battle to secure back-to-back victories, following on from his maiden MotoGP™ win in Aragon last time out.
Yamaha's Quartararo still holds a healthy 48-point lead over Bagnaia in the world championship standings, after the Frenchman made a late charge to secure second place ahead of rookie Enea Bastianini.
Quartararo was delighted with his ride, but was full of admiration for Bagnaia's performance at Misano.
"It was so difficult because they were attacking me from all sides and I lost quite a bit of time in the beginning," Quartararo said.
"But I gave it all and sometimes was really close to the ground. I wanted to try for the win but Francesco was on another level today, I don't know how he's doing that.
"At the end we did the job, points in the championship is really important, we still have an advantage so let's stay calm and give congratulations to Francesco because he did an amazing race."
A first MotoGP™ win had been a long time coming for Ducati's Bagnaia, who was delighted to so swiftly add a second, and he acknowledged a strong start was crucial to his victory.
"With soft tyres, maybe I was struggling a bit, but I tried to push in the first two or three laps to make the gap," he said.
"It was very difficult, but I tried to push. The pace was quite close.
"We worked it so perfectly, two big wins in a row is incredible for me. I was targeting to win my first race but always I was missing something and now already two, so I'm very happy."
Bastianini, meanwhile, revelled in a maiden podium appearance.
"It's possible to do this with these bikes, I know the potential," Bastianini said.
"I battled a lot during the race, it was really difficult to close the gap. It was impossible for me to attack these two riders [Bagnaia and Quartararo] today, but it's really nice to have the first podium at Misano, it's amazing for me."