Rinderknech, who is ranked exactly 100th in the world, picked up the biggest win of his career in style as he dispatched of second seed Agut with a comfortable 6-2 6-4 victory
In another upset, world number 155 Hugo Gaston laid down an early marker with a first-set demolition of Delbonis, who lost out to eventual winner Pablo Carreno Busta in the Hamburg European Open semi-finals last week, before he triumphed in three sets, 6-0 6-7 (2-7) 7-6 (7-3).
Fourth seed Cristian Garin cruised past Marc Polmans 6-3 6-0 to wrap the match up in less than an hour and seal his fifth ATP quarter-final of 2021.
Another semi-finalist in Hamburg, Laslo Djere survived a second-set scare to eliminate Zizou Bergs with a 6-2 4-6 6-2 win, which sets up a last-eight tie with Rinderknech.
At the Croatia Open in Umag, fourth seed Richard Gasquet battled past qualifier Alessandro Giannessi to secure a 7-6 (7-4) 6-4 victory.
Top seed Albert Ramos-Vinolas also progressed, winning 7-5 6-4 to eliminate Duje Ajdukovic on his home turf.
Isner served 44 aces but still lost, with the 37-year-old going down 6-7 (4-7) 7-6 (7-3) 7-6 (14-12) in a match that saw neither player break serve at any point, climaxing in a marathon tie-break.
Former world number eight Isner was chasing a 17th singles title, and a first at an indoor tournament, and he saw a match point slide by at 6-5 in the second set.
Wu resisted one of the best serves in tennis history and took the match all the way. The first 22 points of the third-set tie-break went with serve, before Wu hit a super backhand winner to interrupt the sequence. Incredibly, Isner won the next rally to bring it back on serve, but the match then got away from him, and a stray forehand from the American gave Wu the title.
Dallas resident Isner, famed for his 11 hours and five minutes win over Nicolas Mahut at Wimbledon in 2010, featuring a 70-68 final set, said of this loss: "That kind of stunk for me."
Wu said: "It's a very tough match today. I'm not even moving when he serves. I made history here for my country. I'm very proud of myself."
Ymer upset the only player among the four semi-finalists who previously had reached a final, 15th seed Carlos Alcaraz, by a score of 7-5 6-3 as he contested his first ATP semi-final at the North Carolina event.
The 22-year-old Swede, ranked number 90 in the world, knocked off Alcaraz in the second round at this year's Australian Open in their only prior meeting.
Ymer converted all three of his break points against the Spanish teen, who is ranked a career-best number 54 this week.
Ivashka had no trouble disposing of Emil Ruusuvuori 6-2 6-1 in the first semi-final.
The Finn had won 93 per cent of his service games this week entering the match but was broken in four of eight Friday.
Ivashka, meanwhile, did not face a single break point on his own serve as he cruised to victory in 68 minutes.
Last year's Paris Masters champion Rune, who is in the hunt for his first title of the season, beat the Frenchman 7-6 (7-2) 7-6 (7-5) and is yet to drop a set in the tournament.
The 19-year-old looks sharp, but so too does Jannik Sinner. Two years Rune's senior, the Italian made light work of his good friend and compatriot Lorenzo Sonego on Friday.
Sinner took just over 90 minutes to triumph 6-4 6-2 and tee up a semi-final with history-making 18-year-old Arthur Fils.
Fils, the world number 163, beat Quentin Halys to become the youngest Frenchman to reach a tour-level semi-final since Richard Gasquet in 2004.
"I have seen him [Fils] play here at this tournament," Sinner said of Fils, as quoted by the ATP Tour's official website.
"He is very strong physically already. He understands the game very well. He started off the year very well, so it is going to be an interesting match for sure."
Sinner will be the favourite despite Fils' hot streak, while Rune will go up against Maxime Cressy in a rematch of their Australian Open second-round match.
Cressy went down 7-5 6-4 6-4 in that meeting in Melbourne last month, though has the chance for revenge after seeing off Borna Coric 7-6 (7-2) 6-4.
Italian Sinner beat home hopeful Dennis Novak 6-4 6-2 to set up a tantalising showdown with Casper Ruud.
Should he win that match, Sinner will move ahead of Hubert Hurkacz in the race to qualify for this year's ATP Finals, while victory for Ruud will strengthen the Norwegian's standing.
"It's going to be tricky," said Sinner. "He's in a better position than I am for the race. I think right now it's tough to say and tough to do because in the end you try always not to think about that, but in the end you think about that because you believe."
Zverev was given a sterner test, eventually overcoming Alex de Minaur 6-2 3-6 6-2 in one hour and 42 minutes. The Olympic gold medallist will now face Felix Auger-Aliassime, who fought back from a set down to defeat Cameron Norrie.
Frances Tiafoe came from a set down to upset top seed Stefanos Tsitsipas 3-6 6-3 6-4 and earn a quarter-final meeting with Diego Schwartzman after the Argentine overcame Gael Monfils 7-6 (7-5) 4-6 6-2.
In St Petersburg, home favourite and sixth seed Karen Khachanov lost a gruelling three-set encounter to Marin Cilic.
The Croatian, who won the title in Russia in his last appearance in 2011, was 4-1 down in the deciding set but took all five of the final games to triumph after two and a half hours on court.
"Everybody is playing good. The tournament is great. It's the end of the season, so everybody wants to finish on a great level," said Cilic, who next faces Roberto Bautista Agut. "For me, it was great to play this kind of a match today."
Another Russian, Aslan Karatsev, fell to John Millman 6-3 6-2. Taylor Fritz and Botic van de Zandschulp also progressed in straight sets.
The German world number three was bounced out at Melbourne Park by Denis Shapovalov in straight sets, but he navigated his way safely past Mackenzie McDonald to reach the quarter-finals in Montpellier.
A largely dominant Zverev won 6-2 7-6 (7-5) to set up a clash with Adrian Mannarino in the last eight, and the 24-year-old highlighted how important he felt it was to quickly get back in the swing of things after disappointment in Melbourne.
"I'm going to give myself the best chance to do well in this tournament. But obviously, I'm happy to be back here," he said of the tournament he won in 2017.
"This is a place I really enjoy coming back [to]. After the Australian Open that I had, I wanted to play tournaments before my scheduled tournaments in Acapulco, Indian Wells and Miami. I said Montpellier is the perfect fit for that, and I'm happy to be here."
The same cannot be said for Gael Monfils, who suffered a crushing 6-1 6-2 defeat to Mikael Ymer on home soil.
The Swede was practically flawless throughout, winning a whopping 83 per cent of points on first serve and 89 per cent on second, with Monfils never even sniffing out a single opportunity to break back.
Richard Gasquet is a force to be reckoned with in Montpellier and reached another quarter-final, seeing off South Korean's Kwon Soon-woo 7-5 6-4.
Frenchman Gasquet reached six consecutive finals in Montpellier while in his prime years, being crowned champion in 2013, 2015 and 2016, and finishing runner-up in 2014, 2017 and 2018. Now 35, his last quarter-final appearance in an ATP main tour event came in August at Winston-Salem.
Gasquet's fellow Frenchman Mannarino sank the hopes of defending champion David Goffin, scoring a sparkling 6-4 6-2 victory.
Fourth seed Nikoloz Basilashvili, who lost twice to Andy Murray in Australia last month, this time fell to world number 152 Damir Dzumhur of Bosnia-Herzegovina, sliding to a 6-1 5-7 6-2 defeat. Basilashvili, the world number 21, now has a record of played five, lost five, for the 2022 season.
At the Tata Open Maharashtra in Pune, there was a surprise defeat for Russian top seed Aslan Karatsev. Karatsev won a title in Sydney last month before losing to Mannarino in the third round of the Australian Open, and in his first match since that disappointment he slumped 6-2 7-6 (7-3) to Swedish qualifier Elias Ymer.
Three seeds joined Ymer in the quarter-finals, with Jiri Vesely, Emil Ruusuvuori and Stefano Travaglia all making smooth progress without dropping a set. Vesely faces Ruusuvuori on Friday, while Travaglia awaits Ymer.
World number seven Zverev beat Felix Auger-Aliassime to claim the Cologne Indoors title on October 18 and continued his fine form in the city with a 6-2 6-1 triumph on Sunday.
Schwartzman had denied Auger-Aliassime the chance to avenge his previous defeat but was never a match for in-form Zverev, who hit nine aces – to his opponent's zero – and saved the only break point he faced.
After an even start, Zverev nosed himself ahead with a break of Schwartzman's serve in the fifth game of the opener, with another concession from the Argentine following.
Zverev swiftly wrapped things up with his first set point, though Schwartzman rallied to gain a break point in the opening game of the final set.
It was an opportunity the world number nine failed to grasp, however, and Zverev made him pay with some clinical shots, rounding off the victory – and his second title of 2020 – with a supreme forehand down the line.
The top seed is seeking a 20th tour-level title and has yet to drop a set in his three matches in Montpellier after beating Bublik 6-1 6-3.
Ymer eliminated Gael Monfils and Richard Gasquet en route to the semi-finals, but the world number 83 struggled against Zverev in his third straight loss to the German.
Zverev was triumphant in his last appearance in this tournament five years ago and is the strong favourite heading into Sunday's final with Bublik.
"I am in the final and I am happy about that," Zverev said in his on-court interview. "I played a pretty good match. I think I played one bad game in the whole match.
"Overall I am happy to be in another final, playing against Alex who I have known since I was 12 years old, so hopefully it will be a fun match."
Bublik also claimed a routine win in his semi-final against Filip Krajinovic, the sixth seed prevailing 6-4 6-2 in a little over an hour.
The 24-year-old is through to his fifth ATP Tour final, having most recently gone all the way at the Singapore Open last February, where he lost to Alexei Popyrin.
At the Tata Open Maharashtra, Mikael's older brother Elias Ymer squandered three match points to lose 5-7 7-6 (7-4) 7-5 to Joao Sousa in Pune.
The Swedish qualifier had defied the odds to make it to the semi-finals and took the opening set against Sousa, before recovering from 4-1 down to level up the second set 4-4.
But Sousa edged the tie-break and survived three match points in the 10th game of the deciding set, which he would go on to win.
Sousa will face Emil Ruusuvuori in Sunday's final after the world number 87 overcame Kamil Majchrzak 6-3 7-6 (7-0) earlier in the day.
It marks the first tour final that Ruusuvuori has reached, while Sousa is in the hunt for a fourth title at this level.
The world number three needed just 50 minutes to swat aside Mannarino 6-1 6-0 to set up a last-four match with Mikael Ymer.
Champion at this event in 2017, Zverev's record in Montpellier moved to 9-1 and he has now won seven matches in a row against Mannarino.
Ymer, the world number 83, squandered one match point in his contest with Richard Gasquet but eventually came through 7-5 6-7 (6-8) 6-1.
The best entertainment came in the earlier match between Alexander Bublik and Roberto Bautista Agut, sixth seed Bublik eventually coming through 6-4 2-6 7-6 (7-4) after just over two hours on court.
He will face Filip Krajinovic for a place in the final, the Serbian having beaten Damir Dzumhur in straight sets.
At the Tata Open Maharashtra, rising Italian star Lorenzo Musetti was surprised by world number 95 Kamil Majchrzak.
The Pole, who defeated Musetti's compatriot Andreas Seppi at the Australian Open in straight sets, won 6-2 6-7 (5-7) 6-4 to set up a semi-final against Emil Ruusuvuori.
The other semi-final sees Joao Sousa, into the last four at Tour level for the first time since St Petersburg in 2019, face Elias Ymer.
"I think I played a great match," said Sousa after beating Daniel Altmaier in straight sets. "I was very solid. I knew it was going to be a tough match, so I was prepared to run a lot."
Zverev and Ruud – the number one and two seeds respectively – received byes in the round of 32, with Danish wildcard Rune defeating Jiri Lehecka 7-6 (7-4) 6-3 to advance in Munich on Monday, and Molcan beating fellow Slovakian Norbert Gombos 6-1 3-6 7-6 (9-7).
Teenager Rune had won his opening match in four of his past five tour-level events ahead of the tournament and extended that run with relative ease.
There were no problems for seventh seed Miomir Kecmanovic as he overcame Max Hans Rehberg in straight sets, 6-2 6-3, and he will face Daniel Altmaier in the last 16 after he beat his German compatriot Philipp Kohlschreiber 7-6 (7-5) 3-6 6-1.
Emil Ruusuvuori is also through after beating Japanese opponent Yoshihito Nishioka 7-6 (7-5) 7-5, and the Finn will now go up against the winner of Dan Evans and Maxime Cressy.
At the Estoril Open, Alejandro Davidovich Fokina, who reached the final in Monte Carlo earlier this month, will face fellow Spaniard Bernabe Zapata Miralles next after he overcame Federico Coria 6-4 6-3.
Fifth seed Frances Tiafoe secured a victory against Dusan Lajovic, with the American coming from a set down to win 2-6 7-5 6-0, and up next for him is Nuno Borges in the last 16.
Borges advanced after opponent Pablo Andujar retired hurt in the second set, although the Portuguese was already a set and 3-0 up at the time, while Soonwoo Kwon eased past Benoit Paire in straight sets.
Zverev, beaten by Dominic Thiem in his first grand slam final at the US Open last month, was knocked out of the French Open in disappointing fashion in the fourth round by Jannik Sinner.
The world number seven has responded impressively on home soil this week, dropping just one set en route to Sunday's final.
He followed up with an impressive performance against Auger-Aliassime, winning 6-3 6-3 in just under 80 minutes.
Auger-Aliassime, who is 0-3 against Zverev, has now lost each of his six Tour finals without winning a set.
Zverev, who won 80 per cent of points behind his first serve, assumed control after breaking the Canadian in the opening game and again to lead 5-2.
He handed a break back with consecutive double-faults but secured the first set in the next game and moved 4-2 up in the second to break Auger-Aliassime's resistance.
A heavy forehand from his 20-year-old opponent handed Zverev victory on his first match point, as he secured a 12th Tour title.