This race has been won by an Italian rider in three of the last five editions now, with Bagnaia joining Andrea Dovizioso in 2017 and Danilo Petrucci in 2019 in that group.
Although Ducati star Bagnaia considers Misano his 'home' circuit, he savoured the moment of crossing the line first in front of Italian supporters.
"It's something I have always dreamed of, because winning in Mugello is incredible," he told a news conference.
"Misano is my home grand prix, but this one is the Italian Grand Prix. It's one of the toughest tracks ever, so it's great."
He was greeted by thousands of fans when he climbed off his bike and made his way towards a trackside enclosure.
"I was thinking to throw my helmet, but I knew we would have a penalty if I ride without my helmet, so it was not possible to do it," Bagnaia said.
Bagnaia crashed out when contesting the lead last time out at the French Grand Prix, having won the previous race in Spain.
This was the ideal way to overcome the Le Mans setback, and Bagnaia said: "For sure, for the championship, it was important to take points in this race, but I have to say I was not feeling more pressure.
"We're doing a job where you have to live with pressure. Mistakes can happen, but the good thing is to restart and don't think about your problems, just think about things you enjoy, and I really enjoyed this weekend a lot."
Bagnaia got ahead of early pace-setter Marco Bezzecchi with 15 laps remaining and clung on under pressure from championship leader Quartararo.
Quartararo started sixth on the grid, one place behind Bagnaia, and the Monster Energy Yamaha rider was delighted with that effort.
Last season's champion Quartararo said: "It was basically my best race of my career. I was feeling bad all the weekend and I made an amazing start, the best one, and then I was overtaking, and losing the front, losing the rear. Ducati was overtaking on the straight, and I was overtaking back.
"I think it was the best race. Before the race I was OK, I had nothing to lose because I knew my pace was not so good.
"To be honest, I was running at my best today and I feel so happy."