Down a set when forced off on Friday, top seed Thiem failed to stave off a quarter-final loss once play resumed on Saturday.
Italian qualifier Mager turned his overnight advantage into a 7-6 (7-4) 7-5 victory before again taking to the court later in the day for his semi-final.
The 25-year-old's opponent, lucky loser Attila Balazs, earlier beat Pedro Martinez 2-6 6-4 6-2 but was left clinging onto a place in the tournament when the rain returned, the Hungarian trailing 7-6 (7-4) 3-3 against Mager.
The winner will likely face Cristian Garin in the final after the Chilean third seed opened up a 6-4 4-4 lead over Borna Coric in the other postponed semi-final.
Poor conditions also interrupted the Delray Beach Open, where Milos Raonic was unable to get underway against Reilly Opelka.
The big servers had their semi-final rescheduled for Sunday and will compete for a spot in the decider against Yoshihito Nishioka, who battled from a set down to defeat Ugo Humbert 1-6 6-4 6-0.
Nishioka has reached the final despite dropping the opener in three of his four matches at the ATP 250 event.
"After the first set I just figured out how to play against him and just kept trying to do it and then it worked," he said, as quoted by the ATP Tour.
"If I lose the first set it's okay, I just figure out how he's going to play, how I have to play against him and then from the second set I say, 'Okay, let's do it this way.'"
Mannarino secured a 7-6 (9-7) 6-4 win on Sunday to reach the second round in his homeland.
The Frenchman roared back from 5-1 down in the first set and rocked Karatsev further by winning the tie-break.
Mannarino then claimed the only break of the second set to advance at the expense of the Russian.
Holger Rune will be his opponent in round two following the Dane's 7-6 (7-4) 7-6 (7-3) defeat of Arthur Rinderknech.
Francisco Cerundolo will do battle with top seed Cameron Norrie in the second round after the Argentine saw off James Duckworth 6-2 3-6 6-3.
There were just two matches in the first round of the Geneva Open, with Tallon Griekspoor and Kamil Majchrzak progressing at the expense of seeds Tommy Paul (6) and Alexander Bublik (8) respectively.
Both players were competing for their first success in Santiago, with fourth seed Martinez appearing in his second tour-level final after losing to Casper Ruud in Kitzbuhel in July.
World number 72 Martinez sat six places above his opponents in the rankings, but it was seventh seed Baez who claimed the first set before the Spaniard bounced back to send the match to a decider.
Martinez carried that second-set impetus into the final set, eventually triumphing after 2 hours and 48 minutes as he condemned Baez to just his third loss in 29 outings in Chile since the start of the 2021 season.
World number 97 Martinez came through Monday's longest match, which lasted two hours and 43 minutes, as a 6-3 6-7 (4-7) 6-4 winner.
Mikael Ymer, who reached the quarter-finals of last week's Swiss Open Gstaad, is also through to the second round in Austria after battling past Pablo Cuevas 6-3 7-5.
Qualifier Jozef Kovalik will face Jiri Vesely for a place in the quarter-finals, meanwhile, after beating ninth seed Jaume Munar in straight sets.
Also through on Monday was lucky loser Carlos Taberner, who took advantage of his second chance by battling from a set down to overcome Thiago Seyboth Wild 3-6 6-3 6-2.
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.
Medvedev will move up to number two in the world in Monday's latest ranking, making him the first player outside of the big four of Roger Federer, Rafael Nadal, Novak Djokovic and Andy Murray to occupy one of the top two positions since Leyton Hewitt in 2005.
The Russian celebrated this achievement with a dogged display to down Herbert in two hours and 11 minutes, saving four of the five break points he faced.
A finalist at the Australian Open, Medvedev is now 14-2 in 2021, with the Open 13 title his sixth on indoor hard courts.
Herbert's strategy of frequently visiting the net was initially picked apart by Medvedev, who only needed one set point in the opener as he threaded a backhand winner expertly down the line.
But the Frenchman applied the pressure in set two, passing up three break points early on before impressing from the baseline to reel off five straight points and claim the breaker from 2-4 behind.
The decider was a tense affair but Herbert's errors at the net came back to undermine his efforts decisively when he served to stay in the match at 5-4.
The 29-year-old has now lost all four of his ATP Finals, while Medvedev again proved himself to be a high-quality operator on such occasions.
The ATP and WTA boards decided to remove ranking points from the third grand slam of the year, with Russian and Belarusian players not allowed to compete due to the invasion of Ukraine.
The 26-year-old Medvedev will miss out from the grass-court major, which starts on June 27, alongside Andrey Rublev, Aryna Sabalenka, Anastasia Pavlyuchenkova and Victoria Azarenka.
But that could aid Medvedev's cause at the end of the tournament as Djokovic is the defending champion and therefore would have more ranking points to lose.
Djokovic has dropped to third in the world rankings, with the injured Alexander Zverev – who made the French Open semi-finals before retiring against Rafael Nadal – in second.
That means it is the first time since November 2003 that none of Djokovic, Rafael Nadal, Roger Federer or Andy Murray have appeared in the top two rankings spots.
Medvedev, who lost in the final of the Rosmalen Grass Court Championship on Sunday, became the first player other than Djokovic, Nadal, Federer or Murray to top the men's rankings in 18 years when he replaced the Serb as number one in February.
In-form Medvedev scored a 6-4 6-4 victory on Saturday as he followed up last Sunday's title in Rotterdam with another trophy success.
Three-time grand slam winner Murray, set to jump 18 places to 52nd in the new rankings, had saved eight match points en route to the Doha final.
He pushed Medvedev hard but could not get the better of a player who will nudge up one spot to seventh in the rankings on Monday.
Murray came back from 0-40 in the opening game to force deuce, but he could not hold serve, and Medvedev soon broke again to lead 4-1.
But back came Murray, and the Briton had a break point to square up the opener at 4-4, only for Medvedev to cling on.
The second set also began with Murray dropping serve, but the 35-year-old levelled up at 3-3 with a backhand winner at the end of a terrific rally.
That raised his hopes of a full-scale fightback and a third title success at this event, plus a first tournament victory since 2019 in Antwerp, but Murray was broken from 40-0 in the ninth game, and that looked to end his hopes.
Murray saved a ninth match point of the week, albeit thanks to a double fault from his opponent, but the Scot could not do so for a 10th time, with a lob from Medvedev giving him a big win and the 17th tour-level title of his career.
Medvedev, the 2021 US Open champion, told Amazon Prime Video in a courtside interview: "It was a very tough match. I'm happy to win, today was a big fight.
"Both of us sometimes were playing bad, then suddenly both of us were playing amazing, and I'm happy to win.
"It was tough for Andy to put the ball through me many times. Now it has to continue, so I'm going to try for as long as I can."
World number one Medvedev fought back from a set down to defeat Aslan Karatsev 3-6 6-4 6-2 and advance to a quarter-final against fifth seed Roberto Bautista Agut, who was granted a walkover after Nick Kyrgios pulled out with an abdominal issue.
The Russian got just 48 per cent of his first serves in during a blustery opening set before improving to 68 per cent in the second and controlling the decider as Karatsev struggled with injury.
"It was tough to play [in] rhythm. It felt like many points were just whoever managed to put the ball in the court was going to win the point," Medvedev said of the tricky conditions.
"It was not easy but I'm happy to win because that's the most important [thing].
"Last year was amazing. I played great tennis. Hopefully I can do the same this year. I like it here in Mallorca, so hopefully I can stay as long as possible in the tournament."
Alongside Medvedev and Bautista Agut, Stefanos Tsitsipas is the only other seed left in the draw after he overcame Ilya Ivashka 6-4 6-4.
Denis Shapovalov was a 6-4 6-1 loser against Benjamin Bonzi, Pablo Carreno Busta went down 6-3 6-4 to Antoine Bellier and Sebastian Baez's meeting with Daniel Altmaier ended in a 6-2 2-6 6-4 defeat for the Argentine.
At the Eastbourne International, second seed Sinner suffered a 6-3 3-6 6-3 loss to Tommy Paul as he made his return from a knee injury sustained at the French Open.
World number 13 Sinner remains without a grass-court win in his ATP Tour career, while Paul will next face defending champion Alex de Minaur, who overcame Lorenzo Sonego 7-6 (7-3) 6-2 in a repeat of last year's final.
Jack Draper defeated fourth seed Diego Schwartzman 7-5 7-6 (7-3) to advance to the quarter-finals and Cameron Norrie cruised past Brandon Nakashima in straight sets.
There were also wins for Maxime Cressy, Alexander Bublik and Taylor Fritz.
Medvedev will replace Novak Djokovic at the top of the rankings next Monday and the Russian could celebrate by claiming a first title of the year in ‘s-Hertogenbosch.
The top seed, who will not compete at Wimbledon due to a ban on Russian and Belarusian players, beat Frenchman Simon 7-5 6-4 on Thursday after saving three set points and storming back from 5-2 down in the opener, setting up a quarter-final against lya Ivashka.
Felix Auger-Aliassime, the second seed, defeated Tallon Griekspoor 7-6 (7-2) 7-6 (7-5), but third seed Taylor Fritz was beaten by wildcard Tim van Rijthoven in straight sets.
Alex de Minaur and Jenson Brooksby also made early exits, losing to French duo Adrian Mannarino and Hugo Gaston respectively.
Marton Fucsovics claimed the scalp of third seed Hurkacz to reach the last 16 at the Stuttgart Open, winning 7-5 6-7 (7-) 6-3
Shapovalov also lost his opening of the grass-court season, Oscar Otte getting the better of the fourth seed 7-6 (8-6) 7-6 (7-4)
There was no such trouble for top seed Stefanos Tsitsipas, who beat Dominic Stricker 6-3 6-4, and Andy Murray accounted for seventh seed Alexander Bublik in straight sets.
The Russian top seed won 3-6 6-3 6-0 on Wednesday, having lost at the first hurdle in Hamburg and at the French Open prior to this ATP 500 event.
Medvedev fired in 22 aces to just three double faults and converted four of his six break points against Gasquet, who had also suffered an early exit at Roland Garros.
World number six Medvedev, the winner of this tournament last year, will face American Reilly Opelka next after winning in 97 minutes.
Opelka was also involved in a battle, recording 26 aces as he eventually saw off qualifier Nino Serdarusic 3-6 7-6 (7-5) 6-2.
Second seed Denis Shapovalov is through, too, having had a more comfortable outing in his 6-2 6-3 win over Viktor Troicki to book a last-16 tie against Ilya Ivashka.
Shapovalov converted all four of his break points and only needed 62 minutes to progress.
"Always great to get the first win, especially against a player like Viktor," said Shapovalov. "We have had a lot of battles before and they have been really long matches, so I'm really happy to get a straight-sets win.
"Indoor tennis is just natural for me. It is what I grew up playing on. It is difficult to have those transitions really quickly from clay court to hard court, but we are having to adapt to these situations quickly now."
Stan Wawrinka, meanwhile, is already in the quarter-finals after ending the challenge of home hope Evgeny Donskoy with a 6-1 3-6 6-3 triumph.
At the Cologne Indoors tournament, sixth seed Hubert Hurkacz saw off Mischa Zverev to reach the quarter-finals with a 6-4 6-3 win, while Dusan Lajovic was one of three seeds to fall at the Sardegna Open.
Second seed Lajovic went down 6-4 7-5 to fellow Serbian Laslo Djere, with Lorenzo Sonego and Pablo Andujar also crashing out.
The world number two was playing in his first final on grass, and took just 63 minutes to win 6-4 6-2 and warm up for Wimbledon in emphatic fashion.
It brings up Medvedev's second title of the season and his 11th in total, though he had failed to progress beyond the quarter-finals in his last five tournaments since winning in Marseille in March.
Medvedev suggested he was clicking into gear after his win over Pablo Carreno Busta on Friday, and he backed up his point on Saturday, cruising to victory without offering up a single break point.
The 25-year-old broke world number 60 Querrey – seeking his first ATP Tour title since 2017 – on three occasions, and an ace, his 10th of the match, sealed victory.
Like at the French Open, Medvedev heads to Wimbledon as the second seed. He is the same half of the draw as 20-time grand slam champion Roger Federer, and has a first-round encounter with Jan-Lennard Struff, who knocked the Russian out of the Halle Open last week.
Medvedev, the top seed, had to come from a set down against his Spanish opponent, winning 3-6 6-3 6-2 to tee up a showdown against Sam Querrey.
The world number two has won 10 ATP Tour titles, but they have all come on hard courts.
"I know that I can play well on grass," said Medvedev, who followed up a quarter-final run at Roland Garros with a first-round defeat to Jan-Lennard Struff at the Halle Open.
"Unfortunately we don't have that many tournaments, only one ATP 500 and one grand slam. It's going to be a special feeling [if I] win my first title on grass.
"I still don't have one on clay, even if I have one final. Adding these titles, especially on different surfaces, can help your confidence and it’s just a great thing for your career."
World number 13 Carreno Busta had looked sharp in successive straight-set wins en route to the semi-finals, and started Friday's encounter in good form.
He had not dropped serve across the first four sets of his campaign in Mallorca and extended that streak by saving three break points in the opening set.
However, Medvedev – who has been drawn in the same half as Roger Federer at Wimbledon – rallied and served out the one-hour, 56-minute victory with an ace.
Querrey, meanwhile, will be going for his first ATP Tour title since 2017 after he cruised to a 6-4 6-3 win over unseeded Adrian Mannarino.
Another player who is hunting for his first Tour triumph on grass is Alex de Minaur, who defeated Soon Woo Kwon 6-3 7-6 (7-2) to progress to the Viking International final.
The world number 18 has won four hard-court titles and will go up against Lorenzo Sonego for the crown in Eastbourne.
Sonego beat De Minaur's compatriot Max Purcell 6-1 3-6 6-1. The Italian triumphed at the Sardegna Open in April.
World number two Medvedev was making his first appearance since March after undergoing a hernia operation and fell to a 6-2 7-6 (7-5) defeat.
The Russian's rustiness was clear in the last-16 tussle as he racked up seven double faults and struggled to make inroads on Gasquet's second serve, with the Frenchman winning 61 per cent of points behind it.
It was the first time Gasquet overcame an opponent ranked in the top two since beating Roger Federer at the 2005 Monte Carlo Masters.
Next up for Gasquet will be Kamil Majchrzak, who beat Marco Cecchinato 6-2 6-3.
At the last-32 stage, Fabio Fognini went down 6-4 6-3 to Thanasi Kokkinakis and Albert Ramos-Vinolas succumbed to a 7-6 (7-5) 6-4 loss against Christopher O'Connell.
Johan Nikles, Nikoloz Basilashvili and Joao Sousa also advanced to the second round.
Top seed Cameron Norrie cruised into the quarter-finals of the Lyon Open by beating Francisco Cerundolo 6-4 6-4.
The Briton will face another Argentinian next in the form of Sebastian Baez, who came from a set down to beat Oscar Otte 5-7 6-4 6-2.
Alex De Minaur also had to rally for a 1-6 6-3 6-2 win against Ugo Humbert, with Yosuke Watanuki awaiting in the last eight after the world number 263 beat Soonwoo Kwon 6-3 6-4.
The 18-year-old Sinner claimed the first top-10 scalp of his career when he beat David Goffin last week, but he did not have enough to hold on against Medvedev.
After world number five Medvedev was brushed aside in a 25-minute first set, the Russian claimed two vital breaks in the second set before taking the decider for a 1-6 6-1 6-2 victory.
Medvedev will next take on Gilles Simon - a Marseille champion in 2007 and 2015 - after the Frenchman overcame Aljaz Bedene 7-6 (8-6) 6-4 to reach the quarter-finals.
Meanwhile, Goffin suffered another upset, going down 6-4 7-6 (7-5) to Belarusian qualifier Egor Gerasimov.
Gerasimov's next opponent, Felix Auger-Aliassime, overcame Pierre-Hugues Herbert in a thrilling encounter, with the youngster coming out on top 6-0 6-7 (6-8) 7-6 (11-9).
Auger-Aliassime's Canadian compatriot Denis Shapovalov also made the last eight as 17 aces helped him defeat two-time finalist Marin Cilic 6-4 4-6 6-2, with the world number 15 to meet Alexander Bublik next.
The world number four and reigning ATP Finals champion triumphed 3-6 6-3 7-5 at Melbourne Park in a match lasting just under two hours and 40 minutes.
That result clinched victory over Germany in the semi-final after Andrey Rublev had earler fought back in style from a set down to defeat Jan-Lennard Struff 3-6 6-1 6-2.
"We're really happy to get the win, that's the most important [thing," Medvedev said. "Tough matches [for] both of us. Both [Andrey and I] lost the first set. [It was] not easy, because we had two days off before the match. But happy we're in the final. That's the most important."
Zverev appeared in control after breaking to go 3-2 ahead in the second set after winning the first, but Medvedev reeled off four games in a row as the world number seven began to struggle with a lower back problem.
"When it's against Sascha and you are 6-3, 3-2, break down, many times you're going to lose a match," Medvedev said. "But I needed to keep my chances alive for the team first of all, for the country. I just tried to stay there, got a bit tight maybe. I just did my job and I'm really happy about it."
Russia will meet Italy in the final following their defeat of Spain, which was secured by Matteo Berrettini's straight-sets win over Roberto Bautista Agut.
After Fabio Fognini saw off Pablo Carreno Busta in three sets, Berrettini - who has beaten three of the top 13 players in the world without dropping a set in this tournament - won 6-3 7-5 to set up Sunday's Russia showdown.
"It's an unbelievable feeling," said a delighted Berrettini, who was absent last year as Italy failed to progress from their group in the inaugural staging of the event. "Last year I couldn't make it, so I'm really happy that the first time that I played we are into the final.
"I'm feeling good. I'm feeling pumped. I'm feeling great to play not just for me, but for my team and for Italy in general. That's what matters the most. I'm really looking forward to playing tomorrow."
SINNER TO FACE FAMILIAR FOE
There will be an all-Italian affair in the final of the Great Ocean Road Open, with Jannik Sinner to face Stefano Travaglia.
In-form Sinner clinched an impressive 7-6 (7-4) 4-6 7-6 (7-4) win over second seed Karen Khachanov, in a three-hour battle, after his compatriot beat Thiago Monteiro 6-3 6-4.
At the Murray River Open, Felix Auger-Aliassime will meet Dan Evans in the final as each look to secure a first ATP Tour title.
Auger-Aliassime needed only 61 minutes to beat Corentin Moutet, while eighth seed Evans required a minute less to ease past Jeremy Chardy.
World number four Medvedev fell to a 6-4 6-7 (7-9) 6-3 loss against three-time major winner Wawrinka, who will next meet Mikael Ymer after his straight-sets win over home favourite Gregoire Barrere.
Second seed Hurkacz did not experience such struggles against Thiem as the Pole cruised to a 6-3 6-4 as he served 12 aces in a dominant performance in Metz.
Hurkacz will face Arthur Rinderknech in the next round after the Frenchman battled to a 7-6 (13-11) 6-3 triumph over fifth seed Nikoloz Basilashvili.
Alexander Bublik, the seventh favourite in France, was also made to work for his progress to the quarter-finals, downing Emil Ruusuvuori 6-7 (4-7) 6-4 6-3.
Fourth seed Holger Rune awaits Bublik after Benjamin Bonzi retired due to injury when 6-4 4-1 down against the Dane.
Lorenzo Sonego coasted through his second-round clash to defeat Gilles Simon 7-6 (7-2) 6-4 to tee up a last-eight clash with Sebastian Korda.
On the eve of the Australian Open, Medvedev boosted his preparations by guiding Russia past Italy thanks to a 6-4 6-2 victory over Matteo Berrettini at Melbourne Park.
It was a dominant display from Russia, who won all eight singles matches they played in the ATP Cup, after Andrey Rublev overpowered Fabio Fognini 6-1 6-2 in the second matchup.
"I want to thank my team. Andrey won all of his matches," Medvedev said. "Thank you for being with me here and lifting this trophy in a few moments."
Medvedev heads in Monday's Australian Open in red-hot form, having won a personal-best 14 successive matches, dating back to the start of last year's Paris Masters.
Of those victories, 10 have come against top-10 opponents as 2019 US Open runner-up Medvedev – seeded fourth for the year's first grand slam – prepares to face Vasek Pospisil on Tuesday.
"It's a really big achievement because I also didn't lose a match. Yeah, 10 matches against Top 10 opponents, didn't lose a match in these 10 matches. It's a big boost in confidence," Medvedev said.
"Even when you lose, you know that you're capable of playing this level, and it helps you for the next time to stand up."
While Italy did not taste team success, Jannik Sinner claimed the Great Ocean Road Open on Sunday.
Sinner overcame countryman Stefano Travaglia 7-6 (7-4) 6-4 to earn his second title following the first all-Italian ATP Tour final since 1988.
The 19-year-old Sinner is the youngest player to win two ATP Tour titles since world number one Novak Djokovic (19) in 2006, while he is also the youngest player to celebrate back-to-back trophies since 20-time grand slam champion Rafael Nadal (19) in 2005.
Elsewhere, eighth seed Daniel Evans defeated Canadian sensation Felix Auger-Aliassime 6-2 6-3 to claim his first tour-level title.
Evans became the first Brit to win an ATP Tour title since Kyle Edmund at the New York Open last February.
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 33-year-old, who triumphed in Montpellier in 2010 and 2014, won 7-5 6-3 to become the eighth French champion in the 10 editions of the tournament since it was relocated from Lyon.
Pospisil, who battled past second seed David Goffin to reach only his second ATP Tour final, failed to make the most of four break points against the Monfils serve in an hour and 37 minutes.
At the Pune Open, Jiri Vesely ended a five-year wait to lift a Tour title after overcoming Egor Gerasimov.
Vesely saved match points in his quarter-final and semi-final to book a showdown with Gerasimov, which he won 7-6 (7-2) 5-7 6-3.
"I have to be realistic. I had a lot of luck in the week, saving six match points [across] two matches in a row," he said.
"I think that happens once in a lifetime, maybe, you never know…
"Two matches in a row, especially in the quarter-finals and semi-finals, is really big."
Vesely is the eighth player since 2013 to save match points in two matches en route to winning a Tour event.
