Bearman, the third-youngest driver to compete in a Formula 1 race, qualified 11th and maintained that position from the start, but was dropped when Lance Stroll's crash brought out an early safety car.
He passed Gunayu Zhou's Sauber, then Nico Hulkenberg's Haas, and finished ahead of fellow Brits Lando Norris in his McLaren and Hamilton in his Mercedes.
He was voted driver of the day by fan vote.
Bearman's father David watched nervously in the Ferrari garage, but among those who congratulated him in the paddock after the surgery was Spaniard Sainz, who was at the Jeddah circuit the day after his surgery. It was included.
Bearman said it was a “difficult race mentally” and that he was “struggling” physically as well.
He added: “I felt like I was a little faster.” [Fernando] with alonso [George] There's a Russell in front of me, but I can't catch it. I lost a lot of time trying to pass Hulkenberg. Hulkenberg used his experience to hold me back for more laps than necessary. That's my fault, but it was a good race.
“This seat needed a little bit of fine-tuning, especially with my lower back and neck hurting, and I didn't have time to focus on that. It was good motivation to finish the race early.”
Bearman, from Chelmsford, Essex, started karting when he was eight years old. He made his single-seater debut in 2020, won the Italian and German F4 titles in 2021, finished third in his debut F3 season in 2022 and was sixth in F2 last year.
He has been a member of the Ferrari Driver Academy since 2021 and drove two practice sessions for the Haas team in F1 last year.