Berrettini, who defeated home favourite Jan-Lennard Struff in the semi-final, grabbed an early break point in the opening set, as the 18-year-old erred by pushing a backhand approach shot into the net.
Auger-Aliassime, who is youngest player in the world's top 100, was unable to take advantage of one of his five chances in the tiebreak, with Berrettini serving well under pressure before taking control of points on his forehand.
Berrettini won all 50 of his service games over the week, claiming more than 89% of his first-serve points in his five matches and becoming the first Italian male grasscourt titlist since Andreas Seppi in Eastbourne in 2011.
The 23-year-old had never tasted victory on grass before, with both his previous wins coming on clay courts in Gstaad and Budapest.
Stuttgart marks Auger-Aliassime's third defeat in as many finals this year after losing out in Rio de Janeiro and Lyon.
(Reporting by Shubham Kalia in Bengaluru, editing by Ian Chadband)
