The highly rated Spanish teenager eventually downed the German wildcard 3-6 6-1 7-6 (7-3).
Kuhn, ranked 259 in the world, was aggressive early on against Alcaraz, and was rewarded with the first set.
But the 19-year-old – playing as top seed in an ATP Tour event for the first time – rallied to ease through the second set, before being made to work much harder to clinch the win on a tie-break.
Alcaraz will now play Filip Krajinovic in the second round after the Serbian also won in a third-set tie-break against Sebastian Baez 6-1 4-6 7-6 (8-6).
Three seeded players crashed out on Tuesday in straight sets, with third favourite Diego Schwartzman losing against Emil Ruusuvuori 7-5 6-4, sixth seed Nikoloz Basilashvili beaten by Aslan Karatsev 6-4 6-0, and eighth seed Holger Rune going down 7-6 (10-8) 7-5 to Tallon Griekspoor.
Fourth seed Pablo Carreno Busta eased through against Luca Nardi 6-2 6-1, while there were also wins for Fabio Fognini, who sealed his 400th career victory, as well as Daniel Elahi Galan, Borna Coric and Francisco Cerundolo.
At the Swiss Open in Gstaad, sixth seed Cristian Garin lost 6-3 6-4 to Yannick Hanfmann and seventh favourite Hugo Gaston fell to Dominic Thiem despite winning the first set, losing 1-6 6-1 7-6 (9-7).
Elsewhere, Frenchman Richard Gasquet beat Roberto Carballes Baena 7-5 6-4, while his compatriot Benoit Paire retired hurt when a set and a break down against Elias Ymer.
A tight game between Swiss pair Dominic Stricker and Marc-Andrea Huesler saw the former prevail 6-7 (2-7) 7-6 (7-2) 6-4, and an all-Spanish affair was similarly close as Jaume Munar defeated Bernabe Zapata Miralles 6-3 3-6 7-5.
There were also wins for qualifiers Juan Pablo Varillas and Nicolas Jarry against Lorenzo Sonego and Thiago Monteiro respectively.
Federer and Krajinovic will do battle on Rod Laver Arena on Wednesday, while Djokovic eased into the third round earlier in the day.
Djokovic said he had spoken to Krajinovic, 27, ahead of the second-round clash with the Swiss great.
"We spoke last night. I thought he fought well to win his opening-round match. He was very close to losing that match. He won in five sets. That was great for his confidence," he told a news conference after beating Tatsuma Ito 6-1 6-4 6-2.
"Obviously today is a completely different match-up against Roger. We did speak a little bit about things that he can do to be, I guess, his best self on the court. Again, it doesn't depend only on him.
"It depends how well Roger starts and how well Roger plays. It can be a very interesting match-up. I think Krajinovic is a very talented player and has been around the Tour for a while, knows Roger's game.
"It just depends on how it starts. It can be a long one. It can be a short one. It's going to be interesting to see."
Djokovic continued his fine start to 2020, winning an eighth straight singles match and setting up a clash with Yoshihito Nishioka.
The 16-time grand slam champion was particularly pleased with his serve after sending down 16 aces and not facing a break point against Ito.
"My serve was working extremely well in first round and second round. That's something I worked on in the off-season," Djokovic said.
"That's one of the priorities I guess of the training sessions, trying to get that I think advantage of winning a lot of easy points on the first serve.
"It has been paying off so far I think in the ATP Cup and here with the two matches."
Federer moved into the third round in Melbourne for the 21st straight year by beating Krajinovic 6-1 6-4 6-1 on Rod Laver Arena.
The Swiss great has never lost before the third round at the year's first grand slam and he retained that record with another strong performance.
Federer quickly put Krajinovic on the back foot and while his level dropped slightly, the 20-time grand slam champion was in fine form to progress after one hour and 32 minutes.
He stamped his authority early, breaking in the second game, which featured a brilliant backhand pass down the line.
It was 4-0 after just 13 minutes as Federer produced a forehand winner to break again and take complete control of the contest and the first set was over soon after.
Federer broke again to begin the second set as his flawless display left Krajinovic struggling to find answers, while he produced a stunning cross-court forehand winner on the run in the fifth game.
But as Federer's incredibly high level started to drop, Krajinovic pounced to break back in the eighth game when the six-time Australian Open champion sent a backhand long.
Federer restored his lead in the next game when Krajinovic netted a backhand volley and made no mistake in serving out the second set.
For the third straight set, Federer broke in Krajinovic's first service game, handed the advantage following a double fault.
Krajinovic needed treatment on his right arm early in the third set, but that did little to slow Federer, who advanced to a meeting with John Millman.
STATISTICAL BREAKDOWN
Roger Federer [3] bt Filip Krajinovic 6-1 6-4 6-1
WINNERS/UNFORCED ERRORS
Federer – 42/14
Krajinovic – 22/24
ACES/DOUBLE FAULTS
Federer – 14/0
Krajinovic – 4/2
BREAK POINTS WON
Federer – 7/14
Krajinovic – 1/3
FIRST SERVE PERCENTAGE
Federer – 69
Krajinovic – 74
PERCENTAGE OF POINTS WON ON FIRST/SECOND SERVE
Federer – 77/62
Krajinovic – 58/20
TOTAL POINTS
Federer – 89
Krajinovic – 56
Federer made serene progress into round three in Melbourne with a 6-1 6-4 6-1 defeat of Filip Krajinovic and will now face Millman, a 6-4 7-5 6-3 victor over Hubert Hurkacz.
Their only previous grand slam meeting came at the 2018 US Open when the Australian won a round of 16 encounter in four sets in blistering heat in New York.
Asked if that match had pushed him further than any other physically, he said: "Yeah, definitely. I don't know anything remotely close. I was just happy it was over.
"I never had that [before]. I rather go back in time [and think I'd like to] play that match again. But I don't have that feeling about that match. I was just happy the US Open was over and I could focus.
"I think it was a combination of many things that went wrong for me on that day, plus the opponent was ready and tough as nails.
"I have no regrets. I tried everything in the match itself, it was just not meant to be that day. I hit the wall."
Conditions in Melbourne have been much kinder for Federer so far, both meteorologically and in terms of the draw.
The third seed was barely tested by first-round opponent Steve Johnson or Krajinovic, but rubbished suggestions that would leave him undercooked.
"I prefer this much more than being overcooked," said the Swiss.
"I prefer it this way because you have always extra left in the tank if you need it."
Federer is likely to have to dig deeper against Millman, especially as he may be in the unusual position of not being the crowd favourite.
Millman has already suggested the match should be moved away from Rod Laver Arena due to the number of corporate fans that inhabit the main show court at Melbourne Park - a request that is likely to fall on deaf ears - but Federer is more than happy to play in a raucous atmosphere.
He said: "I'm always happy when the crowd gets involved.
"I don't choose which court I play on. I don't know if he was joking or if he was serious [about moving].
"You would think a match like this should be played on Rod Laver Arena maybe. I don't know if the other seeds have good match-ups as well.
"He knows Margaret Court Arena better [and] Melbourne Arena but I haven't thought about it.
"I figured this was always going to be on Rod Laver Arena but I'm ready to go anywhere, whatever it takes."
Federer trails Novak Djokovic's record haul of seven titles at Melbourne Park following last year's shock fourth-round exit.
The most successful men's player in history, 20-time grand slam champion Federer has not added to his major tally in two years.
However, the 38-year-old once again looms as a threat and we take a closer look at where the third seed is at ahead of a midweek encounter in Melbourne.
Form and results
Federer did not play a lead-up tournament but there were no signs of rust from the Swiss sensation in the opening round. The veteran produced a polished display against Steve Johnson, hitting 34 winners and 20 unforced errors on Monday.
R1: bt Johnson 6-3 6-2 6-2
Next up
Krajinovic awaits Federer after a gruelling opening to his campaign at Melbourne Park on Tuesday. The 27-year-old Serbian was on court for almost four hours as he outlasted Quentin Halys 7-6 (9-7) 7-6 (7-1) 3-6 4-6 7-5 on Court 22. He will not have much time to recover, with a daunting midweek showdown with an all-time great.
Draw
If, as expected, Federer sees off Krajinovic under the Rod Laver Arena lights, a third-round meeting with either John Millman or 31st seed Hubert Hurkacz is next. A clash with Grigor Dimitrov in the fourth round could also be on the horizon.
What he said
"When you win it's all good. Or even when you make a semis and beyond, you know you're in good shape, plus you're just coming off the off-season so you have the confidence. You have practice, you know, flowing through your body, too. The problem is sometimes when you play too many matches and you don't have that practice block, in a way you're just playing to win, just trying to weasel your way to the next victory and you forget how to properly play tennis. So I think the Australian Open, it's nice if you play well, but there is no drama as if it doesn't go well for the rest of the season. It's worse if later in the season success is not there and you're missing that block of practice and you can't rely on it anymore because it's too far back."
The Italian returned from injury in emphatic fashion at the Stuttgart Open, defeating Andy Murray in the final, before heading to Queen's ahead of the start of the third major of the year.
Berrettini had little trouble negotiating his way through to Sunday's showpiece, dropping just one set throughout the tournament to set up a meeting with Filip Krajinovic.
And despite having to battle in the first set, Berrettini triumphed 7-5 6-4 to retain the title he won last year.
The 26-year-old had an early break cancelled out by Krajinovic but got a crucial second break to take the first set.
A tentative opening followed in the second set, yet Berrettini's patience paid off when he broke in the fifth game and he was able to serve out the victory.
That signified Berrettini's ninth straight win, all on grass, after a three-month injury lay-off.
Berrettini is the first player in the Open Era to win titles in each of his first two appearances at Queen's, and is the eighth repeat champion at the tournament – the other seven players to have achieved that feat are all former world number ones.
"I arrived to Stuttgart, and I wasn't feeling great, I wasn't hitting the ball the way I want it that way I used to do, and I was like 'guys I think it's going be tough' and then it went pretty well," he said after the win," Berrettini said.
"I mean I guess I'm Italian, I'm always complaining!"
Berrettini has also advanced to the final in all four of his past grass-court events, with his only defeat coming against Novak Djokovic at Wimbledon last year.
The world number 10 will now look to go one better this time around at The All England Club.
Spanish second seed Carreno Busta wrapped up a convincing 6-2 6-4 win over Krajinovic of Serbia in one hour and 23 minutes.
Krajinovic, who beat Stefanos Tsitsipas in the quarter-finals, had no answer to Carreno Busta's serve as he won 81 per cent (21/26) of his first-service points.
Carreno Busta broke Krajinovic's serve twice in the first set before he served out.
Krajinovic showed more fight in the second set, but he was unable to create a break chance, and when he offered one to Carreno Busta his opponent seized it.
The victory gave world number 13 Carreno Busta, who did not drop a set in the tournament, his 17th win on clay this season.
Chardy saved six set points before being taken do a decider by Barrere, who passed up six chances to break his opponent and succumbed to a 6-3 3-6 6-3 defeat.
Seventh seed Adrian Mannarino exited after a 6-3 6-4 loss to Alexander Bublik, while Filip Krajinovic – seeded sixth – came from a set down to beat Kyle Edmund 4-6 6-3 6-3.
There were also wins for Fernando Verdasco, Aljaz Bedene, Corentin Moutet and Miomir Kecmanovic.
Following his success over De Minaur at the Moselle Open last week, Giron beat the world number 26 once more as he battled to a 7-6 (7-5) 7-6 (7-2) victory in two hours.
The unseeded American, appearing for the first time in Sofia, rallied from a break down in the second set to reach an ATP Tour quarter-final - where he will meet John Millman - for the fourth time this season.
Millman, who is seeded eighth, lost the first set against qualifier Illya Marchenko but recovered well to comfortably triumph 5-7 7-6 (7-0) 6-3.
However, it was far more straightforward for the other favourites, with top seed Jannik Sinner avoiding a second-set blip to defeat Egor Gerasimov 6-2 7-6 (7-3) and Gael Monfils getting a walkover against Ilya Ivashka.
Number five seed Filip Krajinovic coasted past fellow Serbian Laslo Djere 6-3 6-0 in just over an hour to set up a quarter-final tie with Kamil Majchrzak.
In Thursday's other match, world number 56 James Duckworth smashed Benoit Paire 6-4 6-4 in just an hour and 15 minutes to collect his 11th win in his past 12 outings.
Duckworth, who reached his first ATP Tour final in Nur-Sultan last week, will now challenge defending champion Sinner in the next round.
The world number one advanced to the last eight for a 14th straight year at the tournament with a 7-6 (9-7) 6-3 victory over Krajinovic.
Djokovic had not faced Krajinovic in more than a decade and said it was difficult facing off against one of his closest friends.
"It was one of the longest sets of my career," he said of the first set which lasted an hour and 27 minutes. "It is never easy to play against one of your best friends of so many years.
"We have only played 10 years ago in Serbia and he has changed as a person and as a player. It is rare that we have not played against each other in this decade. We trained several times together and we have played the Davis Cup together; it was good to play against him.
"Janko Tipsarevic [Krajinovic's coach], a Serbian tennis legend, is doing a great job with him. He's in the top 30; I know he's in shape.
"I did not start the game as I wanted. I made many unforced errors, but we must congratulate him for pushing me to the limit."
Djokovic saved five of six break points to seal the win after two hours and seven minutes, setting up a quarter-final clash with Dominik Koepfer.
He attacked Krajinovic's forehand with gusto and delivered a string of drop shots throughout the first set, but that game plan did not come off when holding two set points at 5-4 on his opponent's serve.
Krajinovic then started the tie-break strongly, storming into a 4-1 lead, before Djokovic powered back and took advantage of an error from his opponent to seal the set at the fifth time of asking.
Djokovic wasted little time moving through the gears at the start of the second set, driving forehands down the line to break serve at 1-1. He maintained his advantage to reach 5-3 before breaking serve again to seal the win.
The world number one, competing in the Austrian event for the first time since winning it in 2007, saved a set point in a tie-break during the opener on his way to a 7-6 (8-6) 6-3 triumph.
He had to work hard as Krajinovic, who lost to Djokovic in last month's Italian Open at the last-16 stage, twice broke serve in a tight opener, helping establish a 5-3 lead at one point.
Djokovic hit back in the 10th game to break his opponent for a second time as the opener went to a tie-break, which he edged 8-6 after Krajinovic failed to convert an opportunity when 6-5 up.
The second set was far more straightforward for the 33-year-old, however, as he held serve throughout and broke Krajinovic once to progress through.
"We practiced a few times [together] before coming to Vienna," Djokovic revealed in his on-court interview.
"The draw was tough for us to face each other, but there is always extra pressure and importance to a match when you play someone that you know very well."
Borna Coric is up next for Djokovic after the world number 26 beat Taylor Fritz on the opening day of action.
Elsewhere on Tuesday, Grigor Dimitrov held off fellow top-20 player Karen Khachanov 7-6 (8-6) 6-3 in a competitive match, while Hubert Hurkacz beat Attila Balazs in straight sets.
Dan Evans also advanced to the last 16, where Jurij Rodionov awaits, after Aljaz Bedene withdrew with a thigh complaint when a set down.
Djokovic – who saw a three-year visa ban lifted in November – was playing with Vasek Pospisil in the doubles, and the duo lost 4-6 6-3 10-5 to Tomislav Brkic and Gonzalo Escobar on Monday, but the fans in attendance chanted "Novak" as they welcomed him back following his absence from last year's Australian Open.
The Serbian will face Constant Lestienne in the first round of the men's singles, but second seed Felix Auger-Aliassime is already out after he lost to Alexei Popyrin.
Auger-Aliassime struggled throughout as his Australian opponent, ranked 120th in the world, put in a crowd-pleasing performance to go through 6-4 7-6 (7-5).
Another young star, Holger Rune, is also out after the fifth seed was beaten 2-6 6-4 6-4 by Yoshihito Nishioka.
Quentin Halys set up a potential second-round clash with Djokovic after beating Jordan Thompson in straight sets, while Miomir Kecmanovic, Jack Draper, Roman Safiullin and Thanasi Kokkinakis all progressed.
It was also a bad day for seeds at the Maharashtra Open in Pune, with Alex Molcan beaten 6-2 6-4 by Laslo Djere and Jaume Munar losing 6-4 7-5 to Tallon Griekspoor.
Dutchman Griekspoor will now play Marco Cecchinato after the Italian overcame Nikoloz Basilashvili, and Roberto Carballes Baena set up a last-16 clash against top seed Marin Cilic by defeating fellow Spaniard Bernabe Zapata Miralles.
Filip Krajinovic did make it through a tussle with home favourite Sumit Nagal to set up a meeting with Michael Mmoh, while Benjamin Bonzi will face third seed Emil Ruusuvuori after beating Tseng Chun-hsin.
Djokovic, the world number one, continued his impressive run in New York, where the ATP 1000 event is being held instead of Cincinnati due to the coronavirus pandemic.
The Serbian may have been expecting to have Medvedev awaiting him in the last four, but the Russian exited.
Meanwhile, Stefanos Tsitsipas is also into the semi-finals.
DJOKOVIC RACES THROUGH
Djokovic needed just 62 minutes to breeze past Jan-Lennard Struff 6-3 6-1 to reach a record-equalling eighth Western & Southern Open semi.
The 17-time grand slam champion, who is yet to drop a set at the tournament, improved to 21-0 this year.
Djokovic tied Jimmy Connors, Stefan Edberg, Roger Federer and Bill Talbert's semi-final totals at the ATP 1000 tournament.
BAUTISTA AGUT BEATS MEDVEDEV
Defending champion and last year's US Open runner-up, Medvedev departed in the quarter-finals.
Medvedev, the third seed, was beaten by eighth seed Roberto Bautista Agut 1-6 6-4 6-3.
Bautista Agut has lost eight of his 11 meetings with Djokovic, but won two of their three clashes last year.
TSITSIPAS THROUGH AS RAONIC SAVES MP
Tsitsipas was only on court for 38 minutes before Reilly Opelka retired due to a right knee injury.
Opelka led 6-5 against the fourth seed before retiring due to the injury.
Tsitsipas will face Milos Raonic, who saved a match point before overcoming Filip Krajinovic 4-6 7-6 (7-2) 7-5.
Raonic saved a match point in the 10th game of the third set, winning 11 of the final 13 points to advance.
The world number one needed to triumph in straight sets to finish top of Group Novak Djokovic, but his hopes of progressing were dashed when he lost the second to his German opponent.
While the home favourite did go on to record a 4-0, 1-4, 4-2 victory at the Novak Tennis Centre in Belgrade, it was not enough.
“I am not crying because I got knocked out of the tournament, I am just overwhelmed by emotion because this reminds me of my childhood," Djokovic told the crowd.
"It's been an emotional few days and I want to thank everyone who made this possible. The important thing after this match is that we have one of our own in the final. I love you all and thank you so much for turning up."
Djokovic had opened his campaign at the tournament with a comfortable win over Viktor Troicki on Saturday, though he did come off second best in a point played against a ball boy, who thrilled the crowd with a successful drop shot.
Playing again in the evening session, the 17-time grand slam champion suffered his first loss of 2020, coming out on the wrong side of a deciding set in his contest against Filip Krajinovic.
Djokovic compiled an impressive 18-0 record on the ATP Tour this year, including winning the Australian Open, before the season was suspended due to the coronavirus pandemic.
Krajinovic will instead provide a home presence in Sunday's final, a victory over Troicki enough to see him top the table.
He will go up against Dominic Thiem, who defeated Grigor Dimitrov in straight sets to progress from a group named after his opponent.
Canadian teenager Auger-Aliassime will be seeking his first ATP Tour title after losing all three of his showpiece matches in his breakout campaign last year.
He sealed his place in the final with a 7-6 (7-2) 6-4 victory over Pablo Carreno Busta in a contest lasting one hour and 49 minutes on Saturday.
Unseeded Auger-Aliassime sent down 16 aces, one of which came on match point, and lost only three of his 48 points on first serve, saving all of the four break points he faced in an impressive outing.
"I was serving the best I've ever served in that first set and then played a solid tie-break," he said after reaching his first final on a hard court.
"In the second set, things got interesting with that long third game [when Auger-Aliassime broke]. I was thinking, 'If this goes my way, it might be tough for him'. So, I really pushed to get through."
Monfils is eyeing back-to-back triumphs, having come into this tournament after winning the Open Sud de France on home soil last week.
He defeated Filip Krajinovic in the semi-finals there and repeated the trick against the Serbian this time, winning 6-4 7-6 (7-5) in a display that saw him hit 35 winners.
"It would be great [to win this title again]," said the Frenchman, who like Auger-Aliassime sealed his victory with an ace.
"It would be unbelievable. It would be the first time to win two titles in a row and actually even the first time to win two titles in the same season, so it would be huge for me."
Monfils, who only gave up one break point against Krajinovic, has never played Auger-Aliassime before.
"Felix is a great guy, a humble guy," said Monfils.
"He is very strong, very talented guy. Definitely, I expect a tough match, but a cool match because I think we might see him for a long time in this stage of tournaments."
Huesler arrived in Montpellier on a high from victories over German duo Alexander Zverev and Oscar Otte for Switzerland in Davis Cup qualifiers last weekend.
The left-hander saw off 18-year-old Frenchman Van Assche 6-3 3-6 6-3 and will get a chance to improve his perfect record against Rune to 3-0.
Italian Lorenzo Sonego sent eighth seed Benjamin Bonzi packing with a 6-4 6-3 win, while French-born American Maxime Cressy progressed with a 6-3 6-2 defeat of Antoine Bellier.
Arthur Rinderknech and Quentin Halys also advanced on home soil, along with Marton Fucsovics and Filip Krajinovic.
Big-serving American Isner overcame Filip Krajinovic 7-6 (10-8) 6-4 and will face either Cameron Norrie or Kwon Soon-woo in the round of 32.
Isner is joined in the next round by Evans, who eased past Federico Delbonis 6-3 6-4 to set up a last-32 meeting with either Roberto Bautista Agut or Jenson Brooksby.
Fellow Briton Jack Draper also enjoyed a straight-sets victory, edging out Lorenzo Sonego 6-4 6-3 to book a clash with number six seed Andrey Rublev, who received a bye.
Monday's action will see wildcard Andy Murray face Dominic Thiem and 10th seed Jannik Sinner take on Tommy Paul.
After coming from a set down to force a decider against Lloyd Harris in his opening match in Rome, Karatsev held serve when facing match point in a back-and-forth tie-break.
The Russian had already missed a chance to break for the match but did not fail at the second attempt, completing a 3-6 6-3 7-6 (9-7) win to book a date with world number one Djokovic.
Djokovic will be eager to get back on track after suffering a defeat to Carlos Alcaraz in the semi-finals of the Madrid Open.
Filip Krajinovic's reward for a 7-6 (9-7) 7-6 (7-4) victory over Frances Tiafoe is a showdown with Andrey Rublev, while Cristian Garin will take on the in-form Alcaraz following a 6-3 6-2 success over wildcard Francesco Passaro.
Marin Cilic was the other main-draw winner on Sunday, cruising past Matteo Arnaldi 6-1 6-4 in an hour and 20 minutes.
A memorable week for Krajinovic continued as he saw off fellow Serbian Laslo Djere 6-4 6-2 in his semi-final.
Sixth seed Krajinovic defeated Stefanos Tsitsipas in the quarter-finals and ensured he followed up on that surprise victory with a dominant display against Djere on Saturday.
The victor committed only seven unforced errors in the match, while conceding just two break points in the contest.
Second seed Carreno Busta has not dropped a set all week and kept that run going with a 7-6 (7-2) 6-3 win over Federico Delbonis.
Carreno Busta needed just under two hours to see off a battling Delbonis, with neither player offering up a single break point in a first set that went the distance.
The Spaniard won five straight points to take the tie-break and continued that momentum into the second set when he broke Delbonis twice.
Neither Carreno Busta nor Krajinovic has ever won a tournament at ATP 500 level or above.
Carreno Busta has five career titles, but all of those are at ATP 250 level, losing to Dominic Thiem in his only showpiece appearance at this level at the Rio Open back in 2017.
Krajinovic, meanwhile, has lost all three of the career finals he has reached.
"I enjoy playing here, I feel comfortable here," Carreno Busta said. "It is my most important match this year on Sunday - I need to be really focused until the end.
"[Delbonis] is a really tough player and my level was very good. I probably played better in the second set, but I continued fighting all the time."
At the Nordea Open in Bastad, Sweden, top seed Casper Ruud was comfortable as he defeated Roberto Carballes Baena 6-1 6-4 to earn a place in the final.
Ruud needed just 79 minutes to do the job, breaking Carballes Baena on five occasions.
He has only played two matches – both comfortable wins – to reach the final after a walkover against Henri Laaksonen in the quarters.
Rising star Ruud will bid for his second ATP title of the year and the third of his career against Federico Coria on Sunday.
Coria also had a comfortable last-four tie, seeing off Germany's Yannick Hanfmann 6-2 6 -1, with the win meaning the 29-year-old reached his maiden career tour final.
"I am very happy - it is my first final," said world number 77 Coria, who beat second seed Cristian Garin in the last eight.
"I played the best tennis of my life in this match. It is amazing here in Bastad, it is beautiful."
Bautista Agut lost the first set to Spanish compatriot Pablo Martinez in Kitzbuhel, Austria, and could not complete a comeback despite forcing a decider as he lost 6-4 6-7 (5-7) 7-5.
Top seed Casper Ruud, who won last week in Gstaad to claim his third ATP Tour crown of 2021 and fourth in total, came from 4-2 down in the first set to win 7-5 5-7 6-4 against Mario Vilella Martinez.
Third seed Filip Krajinovic survived a second-set scare to beat Carlos Taberner 6-3 2-6 6-4.
Arthur Rinderknech, who dispatched of fifth seed Federico Delbonis on Tuesday, awaits Krajinovic in the next round.
The other clash on Wednesday saw Sweden's Mikael Ymer cruise past home favourite Alexander Erler 6-2 6-3 to secure a quarter-final berth.
Ymer will now face the thankless task of challenging 22-year-old Ruud for a spot in the semi-finals.
