Bagnaia's sprint win in his home race moved him up to 106 points while VR46 Racing's Bezzecchi is four points behind ahead of Sunday's race.
It was Bagnaia's third sprint win of the season, while he has made the podium in five of the six sprints.
Rain threatened to wreak havoc early on but the sun peeked out from behind the dark clouds at Mugello, although the riders still had to deal with wind and drizzle on sections of the track.
"It was a bit scary in the end with rain in sector two and three," Bagnaia said.
"I just tried to not leave any chance for him (Bezzecchi) to overtake. I really enjoyed today."
Gresini Ducati's Alex Marquez (27) started on the front row but his race lasted barely a few seconds until Brad Binder (27) nudged him on turn one, causing the Spaniard to lose his balance and crash. Binder received a long-lap penalty as a result.
Binder eventually finished outside the top 10 but not before the South African had written his name into the history books by becoming the fastest Grand Prix rider ever, clocking 366.1 kph.
Alex's brother Marc Marquez (30) started well to stay behind pole sitter Bagnaia but he was soon overtaken by both the Pramac Ducatis and the two VR46 Racing riders, dropping down to seventh when Jack Miller (28) also got past him on the Red Bull KTM.
Bezzecchi then made his move to get past the Pramac Ducatis and up to second, giving Bagnaia chase with the two riders separated by just one point in the championship standings going into the sprint.
Bagnaia held on for the win to the delight of the Italian fans in attendance while Jorge Martin (25) edged Pramac team mate Johan Zarco (32) in an intense battle for third. Martin also moved up to third in the championship standings (87 points).
"It was a fantastic sprint. I had pace but I wasn't fast enough in qualifying," said Bezzecchi, who was only seventh-fastest in qualifying.
"I'm confident for the race. Very happy with today and we will concentrate on tomorrow."
