The Spaniard is the only one of the tournament's top four seeds left after Stefanos Tsitsipas of Greece crashed out in a late-night match to France's Ugo Humbert 6-4, 3-6, 7-5.
Alcaraz' nearly two-and-a-half-hour match was ferociously physical, with 33rd-ranked Evans giving as good as he got, leading at one point by three games in the first set.
But over the course of prolonged and sometimes scrappy rallies that left spectators gasping and groaning, the world number two gradually assumed control, comprehensively winning the first-set tiebreaker.
"That was probably one of the toughest matches I've played this year," said the 20-year-old Alcaraz after the match.
"I tried to stay all the time there, waiting for my opportunities. I had to stay strong mentally, stay strong physically... I'm really happy with the level that I played."
Alcaraz will next play Bulgarian Grigor Dimitrov, who earlier overcame a torrential downpour and a well-matched opponent in Russian Karen Khachanov to win 7-6 (8/6), 6-4.
Alcaraz, a two-time Grand Slam winner, is the favourite to take the title in the absence of world number one Novak Djokovic, and is hoping to use his time in China to close the gap on the Serbian at the top of the ATP rankings.
And his pool of main rivals has shrunk as the competition has progressed.
Second seed and defending champion Daniil Medvedev was upset by 26th-ranked Sebastian Korda on Sunday and third seed Holger Rune was taken out a round earlier.
Greece's Tsitsipas joined them in the early hours of Tuesday, after a match in which the 25-year-old never really seemed to find consistent form.
The world number six looked rattled after losing the first set, but regained his composure to answer back with the second.
But as 34th-ranked Humbert drew ahead again in the third, Tsitsipas seemed to lose his cool, talking angrily to himself and hitting a ball high into the air in exasperation.
Humbert held on through a late third-set Greek fightback until Tsitsipas sent the ball into the net at the end of the matchpoint rally.
"At the end it was a little bit tight, I tried to move a bit in the last two games, and I'm very proud I did it," the Frenchman said.
He will next face American JJ Wolf, a challenge he called "not easy".
Also through to the final 16 is fifth seed and world number seven Andrey Rublev, who took out Humbert's compatriot Adrian Mannarino 6-3, 6-0 in just an hour.
There was more Gallic heartbreak for 19-year-old Arthur Fils, who came from a set down against world number 12 Tommy Paul to win a tiebreaker in the second set.
The players were level at the eighth game in the third, but the American snatched the last two to win 6-4, 6-7 (7/9), 6-4.
Paul and Rublev will meet later in the week.
Jannik Sinner, who knocked Alcaraz out of the China Open semi-finals in Beijing last week, will play the United States' Ben Shelton in Tuesday's evening session.
Wildcard Diego Schwartzman also booked a place in the fourth round, knocking out world number eight Taylor Fritz in a thrilling third-set tiebreaker on Monday.
The diminutive Argentinian has seen his ranking slide from eighth in the world to 130th, but played his best tennis to topple American Fritz 6-4, 3-6, 7-6 (7/5).
The rankings and age gaps were hardly noticeable over a three-hour skirmish which saw 31-year-old Schwartzman playing up to the crowd, encouraging them to whoop and cheer for him.
"I think it was a great match," the Argentinian said at the end, profusely thanking the tournament organisers for giving him the wildcard and saying it had improved what was "not his best year".
© 2023 AFP