Rublev holds the final automatic qualification spot for the season-ending tournament in London next month following a 6-2 6-1 win over Cameron Norrie.
The third seed was a cut above Brit Norrie, improving his record to 32 victories and just seven defeats this year, which has included three titles.
Shapovalov, meanwhile, beat Stan Wawrinka 6-4 7-5 in a battle between youth and experience, the 21-year-old Canadian winning 84 per cent of his first-service points.
Milos Raonic defeated fellow seed Karen Khachanov 6-1 7-6 (7-1) and will face Borna Coric in the other semi-final, the Croatian having ousted Reilly Opelka in straight sets.
Top seed Alexander Zverev moved into the last four of the Cologne Indoors on home soil, beating South African qualifier Lloyd Harris 6-4 3-6 6-0.
Zverev will come up against Alejandro Davidovich Fokina in his third semi-final of the year after the unseeded Spaniard got past Dennis Novak 6-3 2-6 6-3.
Roberto Bautista Agut and Felix Auger-Aliassime will do battle for a place in the final following wins over Hubert Hurkacz and Radu Albot respectively.
Marco Cecchinato and Lorenzo Musetti will be hoping to contest an all-Italian Sardegna Open in their homeland after advancing to the last four on Friday, along with Serbian duo Laslo Djere and Danilo Petrovic.
World number eight Bertens defeated teenage qualifier Anastasia Potapova 6-4 7-6 (7-3) having staved off three set points in a second set in which she was 5-2 down.
Bertens will face Ekaterina Alexandrova next after she was handed a walkover when third seed Kvitova withdrew.
Top seed Belinda Bencic was ousted by Maria Sakkari in three sets, with Elena Rybakina beating Oceane Dodin in the other quarter-final.
At the Thailand Open, world number four Elina Svitolina suffered a surprise straight-sets loss to Nao Hibino, who was joined in the semi-finals by Magda Linette, Patricia Maria Tig and Leonie Kung.
Bertens became the first player to win back-to-back titles in St Petersburg, easing to a 6-1 6-3 victory over eighth seed Rybakina.
World number eight Bertens, who was due to face the returning Kim Clijsters in the first round of the Dubai Tennis Championships before withdrawing this weekend, was in tears after losing just one set this week to claim a 10th WTA title.
She saved all five break points she faced, securing a first title this year.
"I never expect any match to be easy. It didn't feel easy, of course, even though the scoreline was. At the end, I felt a little bit nervous, but I was just happy to close it out," second seed Bertens said.
"I just tried to approach every point the same, no matter what the score is. Sometimes, on a break point, you go for a little more on serve, and that's what I did today."
Linette sealed the second WTA Tour title of her career with a 6-3 6-2 defeat of qualifier Leonie Kung in Hua Hin.
Teenager Kung, playing in the main draw of an event at this level for only the second time, failed to break Linette's serve and was made to pay for being unable to hold on three occasions.
World number eight Bertens, who has been confirmed as Kim Clijsters' first opponent in next week's Dubai Tennis Championships, required a decider on Saturday to secure a third successive win over a Russian opponent.
But despite relinquishing control in the second set, Bertens did not let up in the third as she ultimately cruised through to reach her first singles final since October.
Eighth seed Elena Rybakina will be Bertens' opponent in the final, with the 20-year-old advancing to the biggest final of her career so far with a 3-6 7-5 6-1 defeat of Maria Sakkari.
Elsewhere, in the Thailand Open, teenager Leonie Kung got the better of Nao Hibino to make the final in what is just her second WTA Tour main draw event.
The 19-year-old had to come from a break down in the decider on Saturday but ultimately triumphed 7-5 4-6 6-3.
Kung will face world number 42 Magda Linette in the final, with the Pole having overcome Patricia Maria Tig in her semi-final.
The top seed had ended a dismal losing streak with victory over Richard Gasquet in the first round and looked to be on course to advance again when he took the first set against Opelka.
But the 6ft 11in American responded to prevail 2-6 7-5 6-4 after successfully defending four Medvedev break points in the third set.
The world number six, who reached the US Open semi-finals before embarking on this desperate run, is the biggest scalp of Opelka's career.
"It is always a tough match, playing one of the best players in the world in general but especially at home," the victor said. "[It is] a great win for me.
"It was ugly for the first set and a half. I felt like I barely won any points on his serve, but part of that is just because of my opponent. Daniil is an absolute nightmare to play."
Medvedev smashed his racket into the court at the end of another frustrating contest.
Russia's other big names will at least fly the flag, as Andrey Rublev and Karen Khachanov progressed.
Rublev's comeback win over Ugo Humbert was a big one for the third seed, who is closing on a place in the ATP Finals. Canada's Denis Shapovalov is also in the running and remains in the hunt for the title this week.
Alexander Zverev eased through at the Cologne Indoors, beating Fernando Verdasco in straight sets, but Marin Cilic exited at the hands of Alejandro Davidovich Fokina.
Cilic led by a set and a break, then had two opportunities to break back in front at 5-5 in the second, before losing 3-6 7-6 (7-3) 6-2.
At the Sardegna Open, Casper Ruud was the victim of the day's biggest upset.
The third seed's prior five defeats since the ATP Tour returned in August had come against top-20 players, but he went down 6-2 6-1 to 101st-ranked Yannick Hanfmann.
A 6-4 6-4 loss came against a player he once led 13-1 in their career head-to-head, a gap which has now closed to 13-4 after a hat-trick of wins for Spanish left-hander Verdasco.
Following victories for Verdasco at the US Open and Shenzhen Open in 2018, the Madrid man again got the better of the two-time Wimbledon champion, beating the Scot on an indoor hard court for the first time after five previous defeats.
It was a tough draw for Murray, who also struck unlucky at the French Open last month when he was paired with former champion Stan Wawrinka in the first round and also lost in straight sets.
The former world number one had entered the Cologne event, a low-level ATP 250 tournament, in the hope of building up match practice and registering the wins he needs to improve his ranking, which stands at 115 after his battle with injury in recent seasons.
Marin Cilic and Gilles Simon won through to the second round earlier in the day at the German event.
At the St Petersburg Open, Belarusian qualifier Ilya Ivashka survived an on-court meltdown to beat French player Adrian Mannarino 6-3 7-6 (8-6) in the first round.
Trailing 3-2 in the second set, Ivashka insisted on taking a toilet break and was penalised a game on his return to court, for delaying the match.
Ivashka explained to the chair umpire he had asked for a medical timeout because he "wasn't able to stand on court", only to be told such a break could not be used for a toilet trip.
The red mist descended as a seething Ivashka shouted: "That is not possible. It is not possible."
The punishment meant the 26-year-old fell 4-2 behind in the set, but he managed to turn around the situation to progress to the last-16 stage, where Denis Shapovalov or Viktor Troicki will await.
At the same tournament, Russian Andrey Rublev began his first week as a top-10 player by scoring a comfortable 6-2 6-4 win over Canadian Vasek Pospisil.
Milos Raonic, who skipped the French Open where Rublev reached the quarter-finals, fired 21 aces in a 7-6 (7-5) 6-1 win against JJ Wolf.
In Italy, home player Lorenzo Sonego followed up his run to the fourth round of the French Open with a 6-2 7-6 (7-4) opening win over 18-year-old compatriot Giulio Zeppieri at the Sardegna Open.
Ostapenko needed less than an hour to get past Paula Badosa, who caused an upset when the pair met at last year's delayed French Open.
There was to be no Roland Garros repeat for Badosa, though, as she was swept aside 6-2 6-2.
The sixth-seeded Ostapenko started her campaign impressively in Russia, producing 26 winners and just eight unforced errors. Her serve was also in good order, never giving her opponent a chance of a break.
Sasnovich had to work a little harder, rallying from a set down to see off Ana Bogdan 2-6 6-2 6-1. Her reward is a clash with third seed Fiona Ferro, who received a bye through to the second round.
Zvonareva, meanwhile, progressed in straight sets against Arina Rodionova, the Russian dropping just four games during a contest that lasted one hour and 22 minutes.
Victory was sealed at the second opportunity, a sliced backhand into the net by her opponent sending Zvonareva through to the last 32.
Rublev trailed Denis Shapovalov by a set but fought back to prevail 4-6 6-3 6-4 and ensure there will be a home hope in the final.
He saved five of six break points in the process of earning victory over the Canadian, the win moving Rublev ahead of Diego Schwartzman into eighth place in the battle to qualify for the season-ending tournament in London.
His opponent will be 2019 finalist Coric, who will be looking to go one better than last year after he staged a turnaround of his own.
Coric, beaten by Daniil Medvedev in his previous appearance in the final, saw off Milos Raonic 1-6 6-1 6-4.
Alexander Zverev progressed to his second final since the resumption of the ATP Tour at the Cologne Indoors.
Zverev overcame Alejandro Davidovich Fokina 7-5 7-6 (7-3) but was full of praise for the NextGen ATP Finals contender.
"He played much better tennis and I think he's somebody who is going to go up the [FedEx ATP] Rankings very quickly," Zverev said.
"For me he's a great guy as well. He's very talented, extremely good with the hands. I think he's somebody who's going to find his way up and it's going to be interesting to see what the future weeks [hold for him] this year and next year as well."
The German will meet Felix Auger-Aliassime, who recorded a 6-3 1-6 6-3 triumph over Roberto Bautista Agut.
At the Sardegna Open, Marco Cecchinato routed Danilo Petrovic 6-1 6-0 and will face Laslo Djere in the final after Lorenzo Musetti retired in the third set with a right elbow injury. Djere was leading 2-6 6-2 4-1.
A recent US Open quarter-finalist, world number 69 Van de Zandschlup claimed the first top-10 win of his career on Friday.
The 26-year-old also advanced to the semi-finals of an ATP event for the first time.
There, he will face 2011 champion Marin Cilic, who was a 6-4 3-6 6-3 winner over third seed Roberto Bautista Agut.
Denis Shapovalov was another big-name casualty in Russia, the second seed going down 4-6 3-6 against world number 53 Jan-Lennard Struff.
Although, there were better fortunes for fifth seed Taylor Fritz. The Indian Wells semi-finalist is yet to drop a set this week after prevailing 6-4 6-2 against John Millman.
Elsewhere, Matteo Berrettini was the victim of another upset at the Erste Bank Open in Vienna.
The Wimbledon champion went down 1-6 7-6 (7-2) 6-7 (5-7) following a two-hour 40-minute battle with Carlos Alcaraz.
Reaching his first ATP 500 semi-final, the Spanish teenager claimed another big scalp having defeated Stefanos Tsitsipas at Flushing Meadows last month.
However, second seed Alexander Zverev remained on course for a fifth title of the season, as he claimed his 300th tour-level win.
The Australian Open finalist beat Felix Auger-Aliassime 6-4 3-6 6-3, avenging his fourth-round defeat by the Canadian at Wimbledon in July.
Sakkari, the top seed in the tournament, had to go the distance against Irina-Camelia Begu, with the world number seven eventually prevailing 6-4 6-7 (4-7) 6-4.
That victory took Sakkari three hours and four minutes, as she had to fight back from a break down in the deciding set.
However, she is now into a fourth singles final of her career and has gone one better than her previous best run at St Petersburg, which came in 2020 when she reached the semi-finals.
"It was a very tough match. I think Begu played really, really well," Sakkari said.
"The level of the match was super high. I had to come up with some very tough shots and very physical tennis, but I'm very glad I did it, and I'm super excited to be in the final here."
Second seed Kontaveit awaits in Sunday's final, and the Estonian world number nine should be much fresher after only needing an hour and 11 minutes to see off Jelena Ostapenko 6-3 6-4.
Kontaveit has remarkably now won 19 matches in a row indoors in the longest such sequence since Justine Henin celebrated 22 consecutive victories between 2007 and 2010.
"It was a very competitive match. I really had to bring very good energy to come through on top today," Kontaveit said.
"She's a very aggressive player, so I had to be really ready for her big shots and just be as consistent and take my chances when I could. I felt like I did that really well today."
Sakkari and Kontaveit have met 12 times previously, with each player winning six times.
Sinner won his fourth title of what has been an outstanding season for the Italian in Antwerp last weekend and is only 110 points adrift of Hubert Hurkacz in the battle for the final place in the season-ending event in Turin.
Murray did the 20-year-old a favour by knocking Hurkacz out of the ATP 500 tournament in the Austrian capital on Monday and seventh seed Sinner eased to a 6-4 6-2 win over American Opelka two days later.
Sinner, who will overtake Pole Hurkacz if he reaches the semi-finals this week, won 93 per cent of points behind his first serve and did not face a break point in a resounding win and will play Dennis Novak in the second round.
Murray beat Alcaraz at Indian Wells this month, but the 18-year-old rising star from Spain turned the tables on the three-time grand slam champion with a 6-3 6-4 second-round win in Vienna.
Former world number one Murray struggled with his serve and was broken five times as he made an early exit.
Third seed Matteo Berrettini beat Nikoloz Basilashvili 6-7 (5-7) 6-2 6-3 to reach the third round, while Diego Schwartzman, Gael Monfils and Lorenzo Sonego moved into the second round.
In the St Petersburg Open, defending champion Andrey Rublev beat Ilya Ivashka 6-4 6-4 to reach the quarter-finals along with Denis Shapovalov, a 2-6 6-3 6-0 winner against Pablo Andujar.
Jan-Lennard Struff also moved into the last eight, with Karen Khachanov and Marin Cilic securing first-round wins.
The Greek world number seven saw off a stern test from Elise Mertens on Friday, winning 7-6 (9-7) 6-2 to reach the semi-finals.
Sakkari had to salvage three set points in the opener, but eventually came out on top in the tie-break at the first time of asking.
Even with a comfortable lead in the second set, she failed to take the first three match points on offer, but got the fourth over the line to progress to her first semi-final of the season.
Sakkari, 26, previously reached the St Petersburg semi-final in 2020, where she lost to Elena Rybakina.
"When you're down in the score, you try to play more aggressively and [Elise] was playing really good in the last couple of games," Sakkari explained.
"She came up with good serves and solid shots from the baseline. I just fought hard."
Next up
Irina-Camelia Begu stands in the way of Sakkari and a place in the final.
The unseeded Romanian overcame two-time grand slam champion Petra Kvitova in the last 16 and defeated Tereza Martincova 6-4 6-2 in her last-eight tie.
It took just 85 minutes for Begu to secure her place in a fourth semi-final of her career at WTA 500 level or higher, but the first since 2017 in Moscow.
Kontaveit continues remarkable indoor run
World number nine Anett Kontaveit will face Jelena Ostapenko in the other semi-final, after ousting Tokyo 2020 gold medallist Belinda Bencic 7-6 (9-7) 6-2.
After her defeat of Bencic, second seed Kontaveit has now won 18 successive matches at indoor tournaments. She is the first player since Justine Henin in 2010 to go on such a streak.
Last year, the Estonian won titles in Ostrava, Moscow and Cluj-Napoca, which form part of this run.
Ostapenko, meanwhile, beat Aliaksandra Sasnovich 7-6 (7-5) 4-6 6-3 to take her place in the last four. The 2017 French Open champion has only lost to top-10 players so far in 2022 (Paula Badosa and Barbora Krejcikova).
It was neck-and-neck for much of the first set, with neither player losing serve, but Dimitrov appeared to have the upper hand when he got to 6-3 in the tiebreak.
Tsitsipas recovered emphatically, however, the top seed reeling off five successive points to win the set and he went on to book his spot in the second round thanks to a 7-6 (8-6) 6-4 victory. He will face Frances Tiafoe next.
"Grigor is a tough competitor and the level of tennis was really high today. We both competed at our highest [level]," Tsitsipas said afterwards.
"That was great tennis that was being played during the entire match and I got really close to my [best] offence and showed incredible attitude [in] the last game, which was the one that was the most crucial of the match."
Alexander Zverev, seeded second, was also made to work in his first-round clash with Filip Krajinovic.
While he blew the Serbian away in the first set, he found himself 5-2 down in the second as Krajinovic looked set to level the match, but Zverev scrapped his way back and then served to love to win 6-2 7-5. Alex de Minaur awaits the German.
Casper Ruud and Felix Auger-Aliassime, seeded fourth and sixth respectively, were two other high-ranking players who also secured progression, boosting their ATP Finals qualification hopes.
Ruud was pushed hard by Lloyd Harris but eventually outfought the South African in his 7-5 7-6 (7-2) win, while Auger-Alisassime made fairly light work of Ricardas Berankis 6-3 6-2.
Indian Wells champion Cameron Norrie, who is also in with a shot of reaching the ATP Finals, beat Marton Fucsovics 7-6 (7-4) 6-1 to set up a meeting with Auger-Aliassime – the British number one is 11th in the FedEx ATP Race to Turin rankings, one above his next opponent.
At the St Petersburg Open, fifth-seed Taylor Fritz was the highest-ranked player in action and he needed a little over an hour to beat Emil Ruusuvuori 6-1 6-4.
Pablo Andujar defeated Federico Delbonis to set up a meeting with second seed Denis Shapovalov, while Ilya Ivashka beat Laslo Djere for the right to tussle with tournament favourite Andrey Rublev next.
The ATP released a statement on Monday saying an unnamed player is now isolating after testing positive for the virus and a contact-tracing process is underway to notify people who may have come into contact with him.
While they did not confirm Querrey was the player in question, the American no longer features on the draw and his first-round opponent, Denis Shapovalov, is now scheduled to play lucky loser Viktor Troicki.
On court, meanwhile, Stan Wawrinka saved three match points to overcome Dan Evans 3-6 7-6 (7-3) 7-5, wildcard Aslan Karatsev saw off Tennys Sandgren 7-5 3-6 7-5 and Cameron Norrie edged past eighth seed Taylor Fritz 6-4 4-6 6-3.
In Cologne, Oscar Otte beat Jan-Lennard Struff in an all-German clash, while Steve Johnson saw off Filip Krajinovic – the fifth seed – in a deciding set.
At the Forte Village Sardegna Open in Italy, teenager Lorenzo Musetti boosted his burgeoning reputation by beating Pablo Cuevas in straight sets, while Jiri Vesely overcame Kamil Majchrzak.
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.
