He grabbed his only break chance to win the first set and his big serve never allowed Kudla any chance to break back.
Berrettini comfortably held serve throughout, firing 10 aces in total, and broke the American again at 2-2 before cruising to victory with a superb forehand down the line on match point.
In his fourth semi-final this year, Berrettini will now face Jan-Lennard Struff, who won 88% of his first-serve points to beat 2017 winner Lucas Pouille 6-4 6-4.
The German recorded his first win in four meetings with wildcard Pouille to book a place in his first semi-final since the ASB Classic in Auckland in January.
Canadian teenager Felix Auger-Aliassime continued his pursuit of a maiden ATP title with a hard-fought 7-6(3) 6-7(2) 7-6(2) victory over German qualifier Dustin Brown.
Seventh seed Auger-Aliassime saved a match point while trailing 5-4 in the final set before forcing a tiebreak, where he carved out a 5-0 lead and never looked back.
The 18-year-old will meet fellow Canadian Milos Raonic, who is seeded sixth, for a spot in his third ATP final.
Former Wimbledon runner-up Raonic, who missed the entire clay-court season due to a knee injury, showed no rust as he struck 12 aces in a 6-4 6-4 win over Hungarian Marton Fucsovics.
(Reporting by Karolos Grohmann and Hardik Vyas; Editing by Alison Williams and Ken Ferris)
