Britain booked their place in the last eight with a come-from-behind victory over the Czech Republic on Sunday
Sweden were in imperious form in the Spanish capital against the Canadian 2019 finalists who went into battle without their top two players Felix Auger-Aliassime and Denis Shapovalov.
Cilic is just the sixth active player to pass the 20-trophy landmark, joining Roger Federer (103), Rafael Nadal (88), Novak Djokovic (85), Andy Murray (46) and Juan Martin del Potro (22).
Cilic, the 2014 US Open champion, was no match for Karatsev who won the trophy without dropping a set.
In Sunday's final, Kontaveit will bid to win a third title in as many months after beating Marketa Vondrousova 6-3, 6-4 in the other semifinal match.
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Sabalenka was playing in her first tournament since reaching the semi-finals of the US Open last month. She then missed the tournament in Indian Wells, California, after a positive test for the coronavirus.
It will be Prajnesh (ranked 165) who will open the tie for India with a match against Otto Virtanen (ranked 419). It is a splendid opportunity for India to draw first blood as Prajnesh is a superior player.
Fognini finished with 26 winners while between them the pair committed nearly 90 unforced errors. Out of a cumulative total of 25 break points, only nine were converted.
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Daniell and Venus won 7-6 (7/3), 6-2 to continue an excellent Tokyo Games for New Zealand.
Victory over 64th-ranked Katerina Siniakova, who is in the last 32 for the third time in her career, could pitch Ashleigh Barty into a fourth round clash with French Open champion Barbora Krejcikova.
The top-seeded Italian made light of the day's play being delayed by four hours due to torrential rain and exposed the gap between him and the British number one once he came through a tough first set.
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Federer stayed on course for a quarter-final showdown with Djokovic but only after becoming entangled in a rare running dispute with the chair umpire.
Federer, the oldest man in the draw at 39, lost his cool and the set before recovering to defeat former world number three Cilic.
It was his eighth win in eight meetings with the Uzbek and gave him a second round clash against Marin Cilic, another familiar foe he has met 10 times.
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Having slipped to number three in the world, it was always likely that Nadal, the 13-time champion, would face top-ranked Djokovic before the final.
Stricker, last year's French Open junior champion, is ranked 419th. Cilic, who won his only Grand Slam singles title in 2014, is ranked 46th.
The Italian teenager will face the 20-time Grand Slam winner for the second time, having impressed against Nadal in last year's French Open quarter-finals despite losing in straight sets.
Popyrin started off badly, losing the first set 4-6 but charged back and snatched the second 6-0.
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Popyrin let out a huge roar after sealing his victory in front of 250 fans, who were allowed to attend the tournament after passing COVID-19 tests.
Mannarino, who had beaten Albot in their only previous encounter in Sofia last year, could not repeat that feat again as the Moldovan was clearly at his best.