Berrettini, who lost the 2021 final to Novak Djokovic (36), has struggled with an abdominal issue this season and pulled out of the Queen's Club tournament after withdrawing from Monte Carlo, Madrid and the French Open to arrive at Wimbledon undercooked.
After narrowly losing the opening set on Tuesday and being forced to wait a day to resume the match due to persistent rain, he broke for a 5-3 lead in the second set with a rocket forehand winner before drawing level.
In a match of few clear openings, Berrettini raised his level in the third-set tiebreaker to tighten his grip in fading sunlight and on an increasingly slippery surface after falling to the ground earlier.
Play was suspended on Wednesday at 1-1 in the fourth set after Sonego, who beat Berrettini in Stuttgart this year, also took a tumble.
When the duo returned to Court 12 on Thursday, Berrettini cranked up the pressure in the sixth game with some delightful winners on both sides to grab the crucial break and the world number 38 held firm to go through.
Up next for Berrettini is a meeting with Australian 15th seed Alex De Minaur (24) who powered past Belgian qualifier Kimmer Coppejans (29) 6-7, 6-3, 6-3, 7-6.
