However, Cameron Norrie fell short of his best victory of the season when world number five Daniil Medvedev saved match point to win their last-16 match.
A frustrating year has seen Norrie drop to 41st in the world rankings and exit each of the past three Grand Slam tournaments in the first round.
But the 31-year-old showed his key attributes – tenacity, athleticism and controlled aggression – to threaten a huge upset against Medvedev.
Third seed Medvedev, fresh from winning the Almaty title last week, was left angrily punching the surface when he fell a break down in the deciding set.
Norrie served for the match at 5-3 40-30, but Medvedev picked off his opponent’s serve-volley attempt and fought back to win 4-6 6-3 7-6 (7-1).
Second seed Alcaraz also progressed with a 6-1 7-6 (13-11) win over Georgia’s Nikoloz Basilashvili.
Meanwhile, Novak Djokovic’s hopes of qualifying for the ATP Finals were harmed by a second-round defeat at the Swiss Indoors event in Basel.
The 24-time major champion, 39, lost 7-6 (7-4) 5-7 6-7 (5-7) to Germany’s Jan-Lennard Struff, who produced some inspired tennis to beat the Serb for the first time in nine attempts.