The world number one, who reached the final at 's-Hertogenbosch last week only to suffer a shock defeat to Tim van Rijthoven, had not beaten Bautista Agut in three previous matches.
But his duck against the Spaniard is over following a 6-2 6-4 win, which set up a semi-final meeting with Oscar Otte after the German saw off Karen Khachanov in three sets.
"I remember all the matches we had… He was playing some [great] tennis and it was tough for me to win," Medvedev said of his previous meetings with Bautista Agut.
"Today I had my plan, managed to keep it going. Definitely got more edge on the most important points, because he had more break points than me. It was not easy, and I'm happy to win."
Hubert Hurkacz, a Wimbledon semi-finalist last year, is also into the last four after edging Felix Auger-Aliassime in two tie-breaks and will face Nick Kyrgios, who beat Paulo Carreno Busta in straight sets.
Elsewhere, Matteo Berrettini was victorious at the Stuttgart Open and is on course to go back-to-back at the Queen's Club Championships after seeing off Tommy Paul 6-4 6-2 to progress to the semi-finals.
Botic van de Zandschlup is his next opponent, the Dutchman overcoming Alejandro Davidovich Fokina 6-2 6-4.
Meanwhile, Filip Krajinovic had to come from a set down to end Briton Ryan Peniston's run at the quarter-final stage, with his reward a meeting with former US Open champion Marin Cilic, a straight-sets victor over Emil Ruusuvori.
The world number one was forced to save a set point in a tight opener before rallying in a tie-break and sailing through the second set in a 7-6 (7-3) 6-3 win.
Despite falling to a shock defeat to Tim van Rijthoven in 's-Hertogenbosch last week, Medvedev is now 14-2 on grass since a first-round exit at Halle last year, and was delighted to make up for 2021's performance on one of his favoured surfaces.
"I didn't play well in Halle last year, so I'm happy that this year I managed to raise my level," he said after the win.
"As I've always said, I love playing on grass, so I'm happy to show to myself that I'm capable of being in the final of one of the greatest tournaments, especially on grass, and of course I'm looking forward to tomorrow."
Standing between Medvedev and the second grass-court title of his career is Hurkacz, who required two tie-breaks to edge a thrilling contest with Nick Kyrgios, winning 4-6 7-6 (7-2) 7-6 (7-4).
Elsewhere, last year's Wimbledon runner-up Matteo Berrettini remains on course for back-to-back titles at the Queen's Club Championships after a straight-sets win over Botic van de Zandschulp in the final four.
Berrettini overcame a rain stoppage to secure his eighth consecutive victory, securing a 6-4 6-3 win, and delighted after triumphing in challenging conditions.
"It was a really tough match. We stopped for the rain. I had a lot of chances. It was windy again and really tough to play, but I definitely think it was the best match of the week, so I am really happy and looking forward to the final," the Italian said.
Berrettini will face world number 48 Filip Krajinovic in Sunday's final, after the Serb cruised past 2014 US Open champion Marin Cilic 6-3 6-3.
At the Queen's Club Championships, second seed Matteo Berrettini came from a set down to finally see off Denis Kudla, winning 3-6 7-6 (7-5) 6-4.
Defending champion Berrettini was troubled by the world number 82, and was just a tie-break away from suffering an upset, but the Italian came through as he belted down 22 aces in the match.
Berrettini faces Tommy Paul in the quarter-finals after the American beat Stanislas Wawrinka in straight sets, 6-4 6-1.
Ryan Peniston carried on from knocking out number one seed Casper Ruud by beating Francisco Cerundolo 6-0 4-6 6-4, setting up a last eight clash with Filip Krajinovic after he came from behind to defeat Sam Querrey 4-6 6-3 6-4.
The world number nine downed Slovakian Gombos 6-3 6-4 in Montpellier on Friday to stay in contention to win the tournament for a third time.
Filip Krajinovic stands in the way of Monfils and a place in the final after the seventh seed accounted for Gregoire Barrere 6-2 7-5.
Vasek Pospisil moved into the last four when Richard Gasquet retired at 6-1 1-0 down in his homeland due to an abdominal injury.
David Goffin will take on the Canadian after the second seed saw off Pierre-Hugues Herbert 6-4 7-6 (7-5).
James Duckworth reached his maiden ATP Tour semi-final with a 6-3 7-6 (7-4) defeat of qualifier Roberto Marcora at the Pune Open.
The 96-ranked Australia will come up against Egor Gerasimov, who came from a set down to beat Kwon Soon-woo 4-6 7-6 (7-1) 6-4.
Jiri Vesely and Ricardas Berankis will contest the other semi-final after getting past Ilya Ivashka and Yuichi Sugita respectively.
The Frenchman, winner of the Open sud de France last week, made it seven wins in a row by overcoming Evans in one hour and 52 minutes.
Next up in the last four is Filip Krajinovic, who upset the form book to overcome Andrey Rublev 7-6 (7-2) 6-4.
Felix Auger-Aliassime defeated Aljaz Bedene and will face Pablo Carreno Busta, who needed three sets to see off Jannik Sinner, in the other semi-final.
Seeking his third title at the event, world number nine Monfils triumphed 7-6 (7-4) 6-2 in 82 minutes against the Serbian.
Monfils saved all three break points against Krajinovic in an impressive victory that maintains France's perfect record of ensuring a home player reaches the final of the Montpellier tournament.
The 2010 and 2014 champion will meet Pospisil on Sunday after the Canadian defeated David Goffin in three sets.
Goffin served for the match in the decider but lost three decisive games in a row as Pospisil triumphed 6-3 1-6 7-5 in two hours and 21 minutes.
At the Pune Open, Australia's James Duckworth was beaten 7-6 (7-2) 6-4 by Egor Gerasimov in the semi-finals.
The Belarusian dropped only five points behind his first serve as he reached a maiden ATP Tour final, where he will face Jiri Vesely.
Vesely saved match points for the second round in a row, outlasting second seed Ricardas Berankis 6-7 (8-10) 7-6 (7-3) 7-6 (9-7) in a draining encounter to secure a first final in nearly five years.
Competing in his first tournament since February, Nadal has looked in fine form in Rome and followed up Wednesday's impressive 6-1 6-1 dismantling of Pablo Carreno Busta with another encouraging display, beating Lajovic 6-1 6-3.
Lajovic did show some fight during the early exchanges, responding well to a break of serve by breaking back – and to love.
But a marathon game, which included six instances of deuce, followed and Nadal prevailed to go 3-1 up, before going on to lose just four more points when closing out the opening set.
Lajovic looked set to lose with a whimper when successive breaks gave Nadal a 4-0 lead in the second, and although the former responded by winning three games on the bounce, he had given himself too much to do and the Spaniard cruised to victory.
Nadal was a class above for much of the contest, cleverly pulling the Serbian this way and that, and the world number two does not think he could be doing much better.
"I played I think a very positive level of tennis. Of course it needs to keep improving," Nadal said. "I need to keep working on a couple of things that are not coming automatically, but I can't ask for more.
"[It was] another great evening for me against another good opponent. Can't complain at all. Much better [than] what I expected.
"The first set was 6-1, but a super-tough beginning of the match. A lot of good points. I'm very happy, it's an important victory for me after such a long time. To start the tournament with these two victories is great news."
Earlier in the day, world number one Djokovic felt he was "pushed to the limit" by fellow Serbian Filip Krajinovic as he won 7-6 (9-7) 6-3 to reach the last eight in the tournament for a 14th successive year.
It was the first time in more than a decade that the two friends had met on the court and Djokovic was made to work particularly hard, saving five of six break points over the course of the contest and fighting back from 4-1 down in the tie-break before ultimately outlasting his compatriot.
Djokovic's next opponent will be Dominik Koepfer, who dealt with Lorenzo Musetti in relatively comfortable fashion, winning 6-4 6-0.
Fourth seed Matteo Berrettini was pushed all the way by fellow Italian Stefano Travaglia to secure his spot in the next round, coming through a tense 7-6 (7-5) 7-6 (7-1) to set up a meeting with Casper Ruud, who beat Marin Cilic 6-2 7-6 (8-6).
Eighth seed Diego Schwartzman was given a run for his money by Poland's Hubert Hurkacz, but the Argentinian came from behind to prevail 3-6 6-2 6-4.
He will be up next for Nadal, while the other quarter-final will be contested between Grigor Dimitrov and Denis Shapovalov, both of whom came through three-setters on Friday.
Nishikori trailed 6-4 4-2 and was forced to break serve as Guido Pella attempted to close out the match in the second set, before sensationally rallying to a 4-6 7-6 (7-4) 6-2 win on Monday.
A two-time champion at the ATP 500 tournament on the Barcelona clay, Nishikori broke serve on three occasions in the final set en route to the second round.
"He had the match today at 6-5, serving [for the match]," said Nishikori. "He was much better in the first and second [sets] and 3-0 up in the tie-break. I don't know how I fought through. [In the] third set, I was playing much better.
"I was making so many unforced errors in the first and second [sets]. Maybe he got a little bit tired and I was playing strong in the third set. I want to take that to the next round… The way I fought today and the way I played in the third set was good."
Next up for 2014 US Open finalist Nishikori is 13th seed Cristian Garin.
Ilya Ivashka topped Tallon Griekspoor 6-3 6-1 and the qualifier's reward is a showdown with top seed and 20-time grand slam champion Rafael Nadal.
Cameron Norrie, Pablo Andujar, Jeremy Chardy, Pierre-Hugues Herbert, Jaume Munar, Federico Gaio, Egor Gerasimov and Bernabe Zapata Miralles all advanced to the last 32.
At the Serbia Open, seeds Filip Krajinovic and John Millman booked their spots in the round of 16.
With the ATP 250 tournament being staged for the first time since 2012 and headlined by world number one Novak Djokovic, Serbian fifth seed Krajinovic overcame Stefano Travaglia 7-5 5-7 6-3 in a Belgrade rollercoaster.
Millman – the Australian seventh seed – took down local wildcard Danilo Petrovic 7-5 6-4 as Marco Cecchinato and Nikola Milojevic won through.
The number two seed got off to a rocky start, finding himself 5-2 down in the first set before dramatically turning the tide, winning five straight games.
Rublev's first serve percentage improved from 49 to 58 in the second set as he stepped up his game against his Serbian opponent.
"Filip is one of my good friends, and we always have tough battles," Rublev said after his win. "So, today I was going on court thinking that it was going to be a really tough match, and when he started the way he did, I didn't know what to do because he was playing so good.
"Somehow I calmed myself and said 'OK, restart at the bottom and raise my level', and I started to play much, much better. I was able to turn the match around and finish the match in a good way."
He will face Alejandro Davidovich Fokina in the second round after the Spaniard took just 52 minutes to beat Malek Jaziri 6-2 6-0, converting all five of his break points as he strolled to victory.
Seventh seed Alexander Zverev had to come from behind to beat Jiri Lehecka 4-6 6-3 6-4, while Tallon Griekspoor set up a second-round clash with top seed Novak Djokovic after the Dutchman beat Constant Lestienne 6-4 3-6 6-2.
World number 14 Ruud is targeting a third successive ATP title, having also captured the Swedish Open and Swiss Open earlier this month.
It has been a timely return to form for the Norwegian, who suffered a shock defeat to Australia's Jordan Thompson at Wimbledon at the end of June.
Although he was in danger of seeing his nine-match winning streak come to an end in Kitzbuhel, after losing the opening set against Swedish opponent Ymer.
Ruud, who also triumphed at the Geneva Open in May, was then taken to a tie-break in the second ser by the world number 99, but held his nerve to tee up a decider.
It was one-way traffic from there with the 22-year-old dominating play to set up a last-four clash with Arthur Rinderknech, who hit five aces as he overcame third seed Filip Krajinovic 6-4 6-1.
Meanwhile, Daniel Altmaier's place in the semi-finals was secured with a 6-1 6-7 (5-7) 6-3 win over Gianluca Mager.
The world number 135, who reached the fourth round of last year's French Open, will play Pedro Martinez in the semi-finals after the Spaniard saw off Jozef Kovalik 6-2 6-2.
Home favourite Struff made it to the last eight of the clay-court tournament for the fourth time in his career with a 7-6 (7-3) 6-7 (0-7) 6-2 triumph over German countryman Dominik Koepfer, who had little to celebrate on his 27th birthday in Munich.
Struff recovered from 4-2 down to take the first set and racked up four straight games to seal the deciding set. He served 11 aces and staved off five break points in a match lasting two hours and 39 minutes.
"I am very, very happy that I turned around the first set," seventh seed Struff said in his on-court interview.
"I played a not good second-set tie-break. Before [that] the set was okay, but I couldn't lock into his service games that much.
"I am very happy that I broke him I the third set and I am very happy to be through. Dominik is a good guy and a very good player."
Fourth seed Krajinovic stands in the way of Struff and a last-four berth, with the Serbian handed a walkover after last-16 opponent Yannick Hanfmann pulled out with a neck injury.
Nikoloz Basilashvili, seeded fifth, defeated Daniel Elahi Galan 6-4 6-2 to set up a last-eight clash with lucky loser Norbert Gombos, who overcame Federico Coria 6-4 6-1.
At the Estoril Open there was a battle between music collaborators as top seed Denis Shapovalov faced off against Corentin Moutet.
The duo were welcomed onto the court by the track 'Drip', which they released together last year.
On the court, it was Frenchman Moutet who managed to snare an upset victory in a 6-4 2-6 6-4 triumph against the Canadian, to score a second top-20 win of the year.
"It was a very close match," Moutet said. "I'm lucky that I won at the end. A few points decided the winner."
Next up is Albert Ramos-Vinolas, who defeated Pierre-Hugues Herbert 6-2 7-6 (7-3).
Cameron Norrie outlasted wildcard Pedro Martinez 4-6 7-6 (7-1) 7-5 to book a quarter-final against second seed Cristian Garin, who never took to the court as opponent Richard Gasquet withdrew with a left adductor problem.
The world number three claimed the opening set after dominating a tie-break but was pegged back in the second, meaning a decider was required to reveal the inaugural champion.
Thiem crucially recorded a break in the third game before holding his serve to love, pushing him to the brink of glory.
While Krajinovic, who had reached the final at the expense of Novak Djokovic, delayed the inevitable by winning the next game, the Austrian served out for a 4-3 (7-2) 2-4 4-2 victory.
Djokovic had seen his hopes of success on home soil dashed when he finished second in his group, a defeat to Krajinovic during Saturday's second session of play proving costly.
While the world number one did go on to record a 4-0 1-4 4-2 win over Alexander Zverev at the Novak Tennis Centre on Sunday, it was not enough.
The eight-player tournament was the opening leg of the Adria Tour, with the next to be staged in Zadar in Croatia on June 21-22.
A planned stop in Montenegro on June 27-28 was cancelled due to restrictions imposed because of the coronavirus pandemic, though the schedule will still finish in Bosnia on the opening weekend in July.
The Adria Tour concludes on July 5, as Djokovic takes on Damir Dzumhur in an exhibition match in Sarajevo.
World number 84 Ruusuvuori saved a set point in the first-set tie-break on his way to a 7-6 (8-6) 6-4 victory and will now face Ilya Ivashka for a place in the semi-finals.
There was nearly another upset as home hopeful Alexander Bublik, seeded second, had to recover from a set down to overcome Miomir Kecmanovic 2-6 6-3 7-5.
Carlos Taberner awaits Bublik in the next round after the Spaniard beat Egor Gerasimov 5-7 7-6(5) 7-5.
Kwon Soon-woo and James Duckworth saw off Dusan Lajovic and Filip Krajinovic respectively in straight sets to remain a course for glory.
At the Moselle Open in Metz, meanwhile, Gael Monfils took out Philipp Kohlschreiber 7-6(2) 6-4 to reach the quarter-finals on home soil.
Tournament favourite Hubert Hurkacz made light work of 2016 champion Lucas Pouille with a 6-2 6-3 victory to set up a meeting with Andy Murray in the quarter-finals.
Elsewhere on Thursday, German qualifier Peter Gojowczyk proved too strong for Karen Khachanov and will now face Marcos Giron, who upset fourth seed Alex de Minaur.
The world number four made a fast start to his match against Filip Krajinovic, winning the opening five games, but fell away to lose in three sets after an hour and 59 minutes.
Tsitsipas is due to represent Greece at the behind-closed-doors Games in Japan, where he will be among the medal favourites.
His racket bizarrely fell apart in the second set against Krajinovic, with Tsitsipas left clutching just the handle as the head broke off when he attempted a backhand.
Despite reaching for a replacement racket, Tsitsipas could not get the better of his 44th-ranked Serbian opponent.
Krajinovic said, according to the ATP website: "He started really well, really aggressively. I could not find my game, could not find my serve, he was overpowering me. But at the end of the first set, I started to feel better, I was going for my shots.
"It paid off in the end. I am happy to beat Tsitsipas, he is an amazing player. I always play well here, and I hope I keep playing well here."
Krajinovic advances to take on a fellow Serbian, Laslo Djere, in the semi-finals, after Djere swept to a 6-2 6-2 win over Georgian Nikoloz Basilashvili.
Spanish second seed Pablo Carreno Busta prevented a third Serbian reaching the final four, beating Dusan Lajovic 7-6 (7-4) 6-3, and he will face Federico Delbonis on Saturday.
At the Nordea Open in Bastad, Sweden, top seed Casper Ruud had his path to the semi-finals smoothed by the withdrawal of scheduled opponent Henri Laaksonen due to injury.
That walkover means Norwegian Ruud will next tackle Roberto Carballes Baena, who beat Slovakian Norbert Gombos 6-4 6-2.
Chilean second seed Cristian Garin bowed out, beaten 6-4 4-6 6-2 by Argentinian Federico Coria. Coria's semi-final opponent will be Germany's Yannick Hanfmann, a 6-4 6-3 victor over French qualifier Arthur Rinderknech.
After top seed Daniil Medvedev departed the competition a day earlier, Tsitsipas and David Goffin - seeded second and fourth respectively - each suffered upsets to blow the bottom half of the draw wide open.
Slovenia's Aljaz Bedene recorded the biggest win of his career as he cut down Tsitsipas in straight sets, his second triumph over a top-10 player clinched by a 7-5 6-4 scoreline.
"I tried to stay focused, and I delivered," Bedene said shortly after a stunning winner down the line saw him successfully serve out for the match.
"I actually served really well when it was important and kept my cool really, because I was feeling that he [Tsitsipas] was pressuring sometimes.
"I had to stay focused and cool and play my shots, and I delivered. I'm happy with that."
The world number 52 saved five break points in the opener before claiming his first opportunity, and he conceded: "I think he [Tsitsipas] was probably the better player for most of the first set.
"He was serving really well, and I didn't play my game - especially on his service points. I stayed tough, which I had to do, otherwise it would go the other way. I guess the break gave me a boost of confidence."
Bedene will play Felix Auger-Aliassime in the quarter-finals, with the winner potentially meeting NextGen champion Sinner - matched with Pablo Carreno Busta - in the last four.
Sinner, still just 18, came up with 27 winners to see off 10th-ranked Goffin 7-6 (9-7) 7-5.
"I feel great, especially now in this moment," the Italian said, according to quotes on the ATP Tour website. "It was not easy playing against him. He is very solid, so you sometimes go for a winner or change the rhythm.
"It feels like a normal victory, but sometimes you play better than others. It's all about improving and testing where you are."
Reigning champion Gael Monfils prolonged his title defence, beating countryman Gilles Simon 6-4 6-1.
Seventh seed Andrey Rublev also advanced, while Vasek Pospisil could not build on his shock defeat of Medvedev, going down 6-4 7-6 (9-7) to Filip Krajinovic.
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.
