The 27-year-old Italian rider for Aprilia also set a MotoGP record for consecutive laps led with 121 in taking the 20-lap showdown at Circuit of the Americas in Austin, Texas.
Bezzecchi started second behind Italian pole-sitter Fabio Di Giannantonio, who rides for Valentino Rossi's VR46 team, but the Ducati rider faded quickly to fifth as Bezzecchi seized the lead and kept it to the finish.
In leading the first three laps, he broke the previous record for most led in a row of 103 set by Spaniard Jorge Lorenzo of Yamaha in 2015.
His winning time of 40 minutes 50.653 seconds was 2.036 seconds ahead of runner-up Aprilia teammate Jorge Martin of Spain, who won Saturday's sprint race to take the riders' lead by a point. Spain's Pedro Acosta of KTM was third.
Bezzecchi is the first rider since Spain's Marc Marquez in 2014 to win the first three races of a season, Marquez having taken 10 in a row in his run.
"I'm happy. I'm very happy," said Bezzecchi.
"Yesterday I made a mistake, so it was very important to make a good race today."
He praised the crowd, saying of his supporters, "I was very sad, and they gave me a push to bounce back today."
Bezzecchi seized an 81-77 lead over 2024 world champion Martin in the season points standings.
Bezzecchi's victory run also includes last year's closing races at Portugal and Valencia and this year's openers in Thailand and Brazil.
Only reigning world champion Marquez, who was fifth on Sunday just behind Di Giannantonio, and Rossi have had longer modern-era win streaks.