The number one seed dominated his Argentine opponent from the moment the first set went to 3-3, winning nine-straight games from there to ease to victory.
Ruud did need to save four break points in the second game of the second set, but his ability to hold serve seemed to end any resistance that Baez could muster.
The Norwegian will face Frenchman Quentin Halys in the semi-finals after his own straight-sets triumph over Dominic Thiem
Halys reached his first ever ATP Tour semi after recording a 6-1 6-4 win over the former world number three in just one hour and 19 minutes.
The other semi-final will see Miomir Kecmanovic take on Marco Cecchinato after the latter stunned third seed Alejandro Davidovich Fokina in straight sets.
The world number 96 claimed a 7-5 7-6 (7-5) victory in the first meeting between the pair to set up a last-four clash with Kecmanovic, who saw off sixth seed Bernabe Zapata Miralles with a comfortable 7-5 6-2 win.
Elsewhere, Dan Evans is the only seed remaining in the Grand Prix Hassan II as he reached the semi-finals by cruising to a 6-3 7-5 triumph over world number 201 Andrea Vavassori in Marrakech.
Evans will face Roberto Carballes Baena next after the Spaniard toppled fourth seed Tallon Griekspoor 6-3 2-6 6-2.
Second seed Lorenzo Musetti was beaten by Alexandre Muller 6-3 1-6 6-4 in a topsy-turvy encounter, and the Frenchman will now face Pavel Kotov in the final four after the Russian defeated Christopher O'Connell in a thriller, 6-3 6-7 (6-8) 7-6 (7-3).
World number eight Rudd, who claimed the title in Geneva last year with a straight-sets final win over Denis Shapovalov, overcame Kokkinakis 6-4 7-6 (7-3) on Thursday and will now face Opelka.
The American bounced back from losing the second set against Dutchman Tallon Griekspoor to claim a 6-4 3-6 6-3 win as he bids for his third title of 2022, and second seed Ruud said he was excited to pit himself against Opelka after securing his spot in the semi-finals.
"I expect it to be tough," Ruud said. "But I will do my best and see how I can do. I always enjoy playing against Reilly. He is a similar age to myself, and it will be another battle against him – hopefully it will be a good one."
Elsewhere, three-time grand slam semi-finalist Richard Gasquet followed up his shock win over Daniil Medvedev with a 6-2 6-4 victory over Kamil Majchrzak, and will face Joao Sousa for a place in the final after the Portuguese beat Ilya Ivashka 7-5 7-5.
At the Lyon Open, top seed Norrie battled to a 6-4 4-6 7-5 win over Sebastian Baez, spurning three match points before finally downing the Argentinian after a marathon two hours and 40 minutes clash.
The world number 11 will face Holger Rune in his semi-final contest after the 19-year-old came from a set down to beat Manuel Guinard 3-6 6-3 6-4.
The other semi-final in France will see fourth seed Alex de Minaur take on Alex Molcan after the Australian's quarter-final opponent Yosuke Watanuki withdrew after losing the first set 6-4, citing a back issue.
Molcan, meanwhile, downed Federico Coria 6-3 6-2 to reach the final four.
The 2020 US Open winner did not face a single break point in his one-sided 6-2 6-0 victory on Monday, reaching the last 16 after 62 minutes.
It is just the second time in the Austrian's career he has lost as few as two games in a completed ATP-level match, having previously done so against Jaroslav Pospisil in 2013 (in a 6-1 6-1 win).
"Especially with the forehand, it was really good for basically the first time [since my injury]," Thiem said afterwards. "I'm very happy about it. This way is right, the direction is right."
Meanwhile, Argentina's Sebastian Baez was forced to retire when a set down to France's Constant Lestienne, and fifth seed Tommy Paul eased past 16-year-old home hope Martin Landaluce in straight sets.
Only one seed was in action at the Firenze Open on Monday, with Aslan Karatsev advancing courtesy of a walkover following an injury to Tallon Griekspoor.
Korda had eliminated top seed Felix Auger-Aliassime in the quarter-finals in Portugal to set up an all-American last-four clash, and looked on course to reach the final after winning the first set against Tiafoe.
However, the fifth seed roared back to seal a 4-6 7-6 (7-2) 6-4 victory and set up a final encounter with Argentina's Sebastian Baez, who beat Albert Ramos-Vinolas to reach his second tour-level final.
Baez also needed three sets in his semi-final clash after losing a competitive second-set tie-break, but he then produced a scintillating performance to win the decider without dropping a game, winning 6-3 6-7 (7-9) 6-0.
Elsewhere, Danish 19-year-old Rune sealed his first ATP tour final appearance by beating home favourite Oscar Otte 6-4 6-4 at the BMW Open in Munich.
Rune, who has enjoyed a dream week in Bavaria after sensationally downing Alexander Zverev in the last-16 and failing to drop a single set in the tournament, revealed his ambitions to become world number one in the future after the victory.
"It's a pretty unreal feeling," he said of his semi-final win. "I didn't expect this at all coming into this tournament, and I just took it match by match. Obviously, I had a tough draw, playing Zverev in the second round, but I knew it was going to be tough, so I was ready from the beginning, and I'm super happy to be in the final.
"It's getting better and better, I'm improving every day, and this is what matters. I have some goals to be number one in the world, and you have to start somewhere."
Rune will face eighth seed Botic van de Zandschulp in the final after the Dutchman rallied to beat Miomir Kecmanovic 2-6 7-6 (7-4) 6-4 in his own final-four encounter.
Auger-Aliassime won just 50 per cent of points behind his first serve as Korda claimed an impressive 6-2 6-2 success over the Canadian in one hour and 29 minutes.
In the semi-finals Korda will take on fellow American Frances Tiafoe, who edged out Alejandro Davidovich Fokina 7-6 (7-5) 5-7 7-5 in a tight encounter.
The other last-four clash will see Albert Ramos Vinolas take on Sebastian Baez.
Ramos Vinolas bested Fernando Verdasco 6-2 6-2 to set up his meeting with Baez after the Argentine rallied from a set down to defeat Richard Gasquet 3-6 6-1 6-4.
At the BMW Open, second seed Ruud fell to Botic van de Zandschulp in the quarter-finals.
The Dutchman won their only previous encounter en route to the last eight at last year's US Open and he triumphed 7-5 6-1 in Munich.
"Maybe the score is easier than it really was," said Van de Zandschulp. "The first set [was] really tight, I think. A great battle in the first one. I had some opportunities to break him in the beginning and didn't take them. Gladly [at] five-all I made the break and held the serve at 6-5.
"[The] second set was a little bit easier, but I think I played really well today."
Next up for Van de Zandschulp is Miomir Kecmanovic, who defeated Nikoloz Basilashvili 7-6 (7-5) 6-2. Holger Rune will continue his impressive run against Oscar Otte in the other semi-final after they overcame Emil Ruusuvuori and Alejandro Tabilo respectively.
Fritz, who at 25-years-old is seeking the fifth ATP singles title of his career, allowed seventh-seed Giron only one break point opportunity for the entire match. Fritz himself only created two such opportunities, and further illustrating the closely-fought nature of the battle, Fritz edged the total point count 86-85.
With the win, Fritz booked his place against China's Yibing Wu in the semi-final after the 23-year-old defeated 34-year-old French veteran Adrian Mannarino 6-3 6-4.
The other semi-final will be an all-American showdown after J.J. Wolf upset second seed Frances Tiafoe 4-6 6-3 6-4, and 37-year-old John Isner proved too much for Ecuador's Emilio Gomez in a 7-6 (10-8) 7-5 victory.
Meanwhile, Spain's Albert Ramos-Vinolas is one match away from a final in his home country after defeating Joao Sousa 6-4 2-6 6-1 in the quarter-final of the Cordoba Open.
Ramos-Vinolas will play Argentina's Federico Coria for a spot in the decider after he emerged victorious 6-3 3-0 (ret) against compatriot Francisco Cerundolo.
Heading into the quarter-finals, Francisco and his brother Juan Manuel Cerundolo were on a collision course to meet in the final, but now both are eliminated after 21-year-old Juan Manuel fell 6-7 (5-7) 6-4 6-0 to Bolivia's Hugo Dellien.
Dellien will play fourth seed Sebastian Baez in the other semi-final after eliminating Chile's Tomas Barrios Vera 6-1 3-6 6-1.
World number two and top overall seed Alcaraz was strong in his 6-4 7-6 (7-0) victory over Serbia's Dusan Lajovic, improving his unbeaten record in 2023 to 6-0.
Alcaraz has his eyes set on his second title win in a row after also emerging triumphant in last week's Argentina Open.
Meanwhile, Norrie had to fight back from an early deficit to eliminate Hugo Delien 4-6 6-1 6-4, with the world number 13 and second seed now boasting eight wins from his past nine matches. The only loss during that stretch was to Alcaraz in the Argentina Open decider.
For a chance to avenge that loss, Norrie will have to beat Bernabe Zapata Miralles after he overcame Albert Ramos-Vinolas 6-4 2-6 6-4 in an all-Spanish quarter-final.
Alcaraz will contend with Nicolas Jarry, after the unseeded Chilean knocked out his second seeded opponent of the tournament, this time getting the better of Sebastian Baez 6-3 7-6 (7-3).
