Sinner reaches back-to-back Wimbledon quarter-finals
Sinner came through 7-6 (7/4), 6-4, 6-3 and will take on 92nd-ranked Roman Safiullin of Russia for a place in the semi-finals.
The 21-year-old Italian fired 42 winners with 12 aces past the 85th-ranked Galan, who mounted a stirring defensive display.
He saved the first 14 break points he faced and 17 of 20 in the entire match.
Galan even broke for the first time in the second set to lead 2-0 but was unable to maintain the brief momentum as Sinner broke twice to open a two-set lead.
The Italian raced to a 5-2 lead in the third set.
Galan, playing in the last 16 of a major for the first time, saved match points in the eighth game but the tie was over when he hit a backhand long in the following game.
"I wasn't feeling great on court. He's a big server so I had to try and win the important points," said Sinner.
The Italian apologised to the crowd for his demeanour on court when he protested to the umpire over calls he claimed were borderline.
"Some calls were tough, sorry guys, it happens. Players get frustrated but this is the sport," he said.
Last year, Sinner squandered a two-set lead to lose in five against eventual champion Novak Djokovic in the quarter-finals.
Tuesday's duel with the unheralded Safiullin will on paper at least be the easiest of his four last-eight clashes at the majors.
At the French Open in 2020, he was defeated by Rafael Nadal before losing to Stefanos Tsitsipas at the Australian Open in 2022 and Carlos Alcaraz at the US Open later that same year.
