Bagnaia was joined on the podium by the two Pramac Racing riders Jorge Martin (25) and Johann Zarco (32) while VR46 Racing's Luca Marini (25) was fourth, as four Ducatis finished in the top four in their home race in Mugello.
With title rival Marco Bezzecchi finishing eighth, Bagnaia's lead is now 21 points and the race winner celebrated his victory with an impromptu barbecue in front of the crowd, wolfing down a hot dog as the fans chanted his name.
"The perfect weekend. I wasn't expecting a race like this... This is one of the best weekends of my life," said Bagnaia, who had the Italian flag draped around his neck.
"Job done and let's move on to next week in Sachsenring (German Grand Prix)."
Red Bull KTM's Jack Miller had a blistering start from the line to surge ahead before turn one but his former team-mate Bagnaia was quick to pick him off and retake the lead on the opening lap.
Martin soon moved up to second, however, while Marini confidently took his place behind the leading pair to make it three Ducatis in the top three.
Miller dropped down the standings when Alex Marquez sped past three riders on his Gresini Ducati, making contact with the angry Australian in a risky overtaking manoeuvre that nearly led to a wipeout.
Alex's brother Marc Marquez started second on the grid but fell to fourth before crashing on lap six to go four consecutive races without finishing for the first time in his career. The Spaniard has yet to finish a race this season and as he slid off at turn 15 and into the gravel, the six-times champion stood over his bike with his arms outstretched in pure frustration.
Marini kept Alex Marquez at bay for as long as he could as they battled it out for the final podium place. But soon after the Spaniard moved up to third, he threw it away with nine laps to go when he lost his balance and crashed out on turn two.
But Marini had no time to take a breather as Zarco reeled him in and rubbed elbows before the Frenchman moved up to third, denying the home fans the opportunity to see two Italians on the podium.
