Tsitsipas will play 22nd-seeded Spaniard Roberto Bautista Agut for a place in the semi-finals.
Leander Paes' hopes of creating a world record in Davis Cup were dashed when the veteran Indian and Vishnu Vardhan lost the third rubber to strong rivals Artem Sitak and Michael Venus, who kept the New Zealand alive in the Asia-Oceania Group I Davis Cup tie.
A summary of the first day's play at the US Open.
Murray, who took a wildcard into the seaside event as a fitness test for next week's Wimbledon, looked sharp on a sun-baked centre court and tasted victory for the first time since beating Benoit Paire in the last 16 of Wimbledon 350 days ago.
Rafael Nadal overcame a temporary blip on his way to victory at the ATP Cup on Saturday
Andy Murray demolished Croatian teenager Borna Coric 6-1, 6-2 in the second round of the Paris Masters on Wednesday to set up a Davis Cup-flavoured clash with Belgium's David Goffin.
Prajnesh, seeded sixth, got the better of Spain's Enrique Lopez Perez 6-3, 6-3 in the men's singles second round.
Showing great mobility, the towering Czech neutralised the potentially tricky world number 25 in a sometimes tetchy two-hour contest on Margaret Court Arena.
PHOTOS from the Wimbledon Championships matches played at the All England Lawn Tennis and Croquet Club, London, on Saturday
Greek third seed Stefanos Tsitsipas battled back from a set down to beat Serbia's Filip Krajinovic 3-6, 6-4, 6-4 in the quarter-finals of the Swiss Indoor championship on Friday. The win took Tsitsipas into his 10th semi-final of the season where he will face top seed Roger Federer, who was handed a walkover after Swiss compatriot Stan Wawrinka withdrew before their quarter-final with a back issue.
Sania Mirza and her Czech partner Barbora Strycova suffered a straight-set loss against Bethanie Mattek-Sands and Lucie Safarova in the summit clash of the WTA Wuhan Open on Saturday. The third seeds lost 1-6 4-6 to the fifth seeded US-Czech pair of Mattek-Sands and Safarova in the finals of the USD 2,589,000 tournament that lasted a little over an hour.
She is the second Swiss player to win the tournament after Martina Hingis won the inaugural edition in 2001.
IMAGES from the French Open semi-finals played at Roland Garros on Friday
The Canadian set the tournament alight with a scintillating, three-set win over Maria Sharapova on Tuesday after her outspoken comments about the Russian returning from her 15-month doping ban, including calling her a cheater.
'Everyone thinks it was a money-related issue, but it wasn't'
Barty had some trouble in the first set against the two-time Australian Open champion and saved three break points at 5-5 to go on to win 7-6(2), 6-3 and level the tie at 1-1.
Second seed Sloane Stephens was shocked 2-6, 6-4, 6-2 by Germany's Andrea Petkovic in the second round of the Citi Open on Wednesday, disrupting the American's buildup to her US Open title defence.
Serena Williams shook off the rust and a feisty challenge from Serbia's Ana Ivanovic to open the defence of her WTA Tour Finals title with a 6-4, 6-4 victory in the opening match of the elite eight-player tournament on Monday.
US Open champion Naomi Osaka fought back tears and rallied from a set down to outlast Zhang Shuai 3-6, 6-4, 7-5 in the China Open quarter-finals on Friday.
Defending champion Rohan Bopanna went down fighting in the thrilling doubles opening round game at the third edition of Tata Open Maharashtra, in Pune, on Wednesday. Playing alongside local boy Arjun Kadhe, the ace Indian player Bopanna dominated the game initially. However, after winning the first set convincingly, the Indian duo couldn't manage to continue the momentum further in the games against French pair of Benoit Paire and Antoine Hoang as they lost the match 3-6, 7-5, 10-7.
Novak Djokovic continued his Wimbledon preparations by beating American Donald Young 6-2, 7-6(9) on Thursday to reach the semi-finals of the Aegon International tournament at Eastbourne.
Novak Djokovic endured a fierce challenge to his Melbourne Park reign before overhauling Dominic Thiem 6-4, 4-6, 2-6, 6-3, 6-4 on Sunday to clinch an eighth Australian Open crown and reclaim the world number one ranking. He captured the decisive break in the third game of the final set, then held firm as Thiem made desperate assaults on his serve. Going for broke in a nerve-shredding final game, the fifth seeded Austrian went for the lines but missed twice to hand Djokovic one of his most hard-earnt triumphs.
Monday was also the first time in more than two decades that India had more than one player in the main draw of a Grand Slam singles, with Prajnesh Gunneswaran losing to world number five Daniil Medvedev in an earlier match.
India's Rohan Bopanna and his Hungarian partner Timea Babos entered the semi-finals of the Australian Open mixed doubles event with a comfortable victory in Melbourne, on Wednesday.
World No 1 Novak Djokovic laid down an early French Open marker when he reached the Monte Carlos Masters final.
Rafael Nadal was kept on Centre Court longer than he would have liked but that did not stop him from putting baby-faced Alex de Minaur firmly in his place with a 6-1, 6-2, 6-4 win in the third round of Wimbledon on Saturday.
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