The world number two triumphed 6-4, 6-2 to set up a clash with either Jannik Sinner or Grigor Dimitrov in the next round.
Alcaraz shook off an early break of serve to overpower the world number nine, eventually seizing an attritional first set with a 40-0 service game.
He then took control, breaking twice without reply in set two before finally forcing Ruud to slice a backhand into the net.
Earlier, third-ranked Daniil Medvedev booked his place in the semi-finals with a 6-4, 3-6, 6-1 victory over France's Ugo Humbert.
An error-strewn first set saw a combined five breaks of serve but Medvedev edged ahead in the ninth game and finished it off with an ace.
Both men were more consistent in set two until the Russian, at deuce, hit back-to-back double faults to hand the crucial break to Humbert.
But Medvedev finally tightened up in the decider, notching two quickfire breaks before seeing out the match on his serve.
The 27-year-old will battle it out with either world number 10 Alexander Zverev for a place in the final.
Medvedev again attributed the see-saw victory to the match balls, which he has said fluff up too quickly and lead to lengthy rallies.
"It's very slow," he told a post-match press conference.
"(On) any other normal hard court with normal balls, no chance I win the match like this. No chance I would lose my serve so much," he added.
"It's great that I managed to still find, in this tough match, these moments of consistency - which was enough to win."
Zverev, ranked number 10, edged a tight encounter with Chilean Nicolas Jarry 6-1, 6-7(5), 6-3.
World number two and tournament favourite Carlos Alcaraz is due to play his quarter-final against Casper Ruud on Monday evening.
Top-ranked men's player Novak Djokovic is not playing in the China tournaments this season.
Swiatek and Gauff progress
In the first round of the women's draw, world number two Iga Swiatek defeated Spain's Sara Sorribes Tormo in straight sets.
The Pole, who recently relinquished her hold on the number-one spot to Aryna Sabalenka, enjoyed significant success at the net on her way to a 6-4, 6-3 victory.
Swiatek will play France's Varvara Gracheva in the second round.
"I feel like I was pretty patient. You have to be patient with her because she's running for every ball," Swiatek said after the match.
"I kind of wanted to just be solid and be intensive but not make too many mistakes with risking.
"I'm pretty happy I could balance that. It just worked, so I'm happy," said the 22-year-old.
Teenage star Coco Gauff survived a minor scare on the way to a 7-5, 6-3 defeat of Russia's Ekaterina Alexandrova.
The US Open champion was 4-0 up but allowed Alexandrova to level before ripping a backhand winner down the line to break serve and take the first set.
She fared better in the second, picking up a break midway through and seeing out the match with ease.
"She was giving me a lot of errors, so I don't think the 4-0 was completely (down to) my tennis," Gauff told a post-match press briefing.
"Once I got to that point, I definitely started making more unforced errors," she said.
"I was able to buckle down when I needed to, but obviously I think in these moments I want to do better at closing out those sets."
World number seven Ons Jabeur beat American Ashlyn Krueger 6-3, 6-4 to set up a second-round match against Ukraine's Marta Kostyuk.
Sabalenka knocked out former Australian Open champion Sofia Kenin on Sunday to seal her spot in the second round.
The China Open is taking place for the first time since 2019 after Beijing abandoned its long-standing zero-Covid policy.
