Under the lights on the stadium court, Williams smashed 39 winners to defeat Azarenka 7-5, 6-3 in a rematch of the 2016 final, which the Belarusian won.
Murray, who suffered an elbow injury in March and made his return from a five-week layoff on Wednesday after a first-round bye, won the opening set in 48 minutes before losing concentration.
The fifth seed's success made it the first time a Japanese male player had reached the last eight at Roland Garros since Jiro Satoh made it to the semi-finals in 1931 and 1933.
As another Grand Slam crown looks set to be snaffled by a man in his thirties this weekend, tennis fans lamenting a dearth of dynamic up-and-comers need not worry, says former world number one Mats Wilander.
Rafael Nadal's return to action came to a shuddering halt on Friday when the Spaniard was beaten by Slovakia's Martin Klizan in a late-night quarter-final duel at the China Open.
The latest tennis rankings have been announced by the ATP and WTA
Top seed Juan Martin del Potro beat Nicolas Almagro of Spain 7-6(7), 7-6(1) in the semi-final of the Japan Open on Saturday to set up a title clash with big-serving Milos Raonic of Canada.
A ruthless Sorana Cirstea took full advantage of Karolina Pliskova's patchy form at the China Open on Thursday, reaching the quarter-finals as she consigned the recently dethroned world number one to a 6-1, 7-5 defeat.
'If one thing seemed clear in this week of very uneven tennis in Melbourne though, the much celebrated golden age of tennis may be over.'
Rafael Nadal continued his perfect run on the North American hardcourts taming Czech Tomas Berdych 7-5, 7-6 (4) at the Western and Southern Open on Saturday to setup a final showdown with big-hitting American John Isner.
US Open, the final Grand Slam of the season, starts Monday, August 28, at Flushing Meadows in New York.
Marin Cilic's debut appearance at the ATP World Tour Finals is fast turning into a nightmare after his second consecutive drubbing at the O2 Arena on Wednesday.
Rafael Nadal is recovering satisfactorily from appendicitis and will continue a course of antibiotics in a bid to be fit for the remainder of the 2014 season, the World No 2's spokesman said on Thursday.
Novak Djokovic began his challenge for a hat-trick of ATP World Tour Finals triumphs in London with a 6-1, 6-1 demolition of Croatia's Marin Cilic.
Andy Murray continued his strong clay court form by booking a place in the semi-finals of the Madrid Open with a 6-4, 7-5 victory over Milos Raonic.
The Big Four were always going to come into the year's first Grand Slam knowing fully well that their days of dominance are drawing to a close, if not already a thing of the past, says Dhruv Munjal.
Switzerland took advantage of Novak Djokovic's absence to open a 2-0 lead over last year's runners-up Serbia in their Davis Cup tie on Friday with Roger Federer and Stanislas Wawrinka winning their singles rubbers.
Federer, who skipped the French Open this year to give his body time to recover from his incredible exploits in the first half of the season which he began by winning an 18th major at the Australian Open, said he hoped Murray would not live to regret battling through the pain barrier.
'I would say winning the US Open has helped me for all these grand slams I have played so far, and I believe the rest of my career' 'It's great for me to hear that even he, and a lot of players around, even ex-players, when they were looking before the tournament started, that they were seeing me as a player that could go quite deep (into the tournament)'
After two weeks of intriguing tennis where the world's best fought hard to assert their dominance on clay, we have the champions out there.
Earlier on Wednesday, Czech Karolina Pliskova was forced to withdraw from the tournament due to a viral illness.
Roger Federer trounced Croatian teenager Borna Coric 6-2, 6-1 at the Dubai Championships on Friday to set up a potential final showdown with world number one Novak Djokovic.
World No 8 Switzerland's Stanislas Wawrinka confirmed, on Monday, his participation in the 19th edition of the Aircel Chennai Open, India's only ATP World Tour tennis event, starting December 30.
Andy Murray and Rafael Nadal were winners but six seeds were beaten in a day of upsets in the second round at the Rogers Cup in Montreal on Thursday.
Tommy Haas kept alive his slim chances of qualifying for next month's ATP World Tour Finals when he edged past near namesake Robin Haase 6-3, 4-6, 6-4 to lift his 15th career title at the Vienna Open on Sunday.
Novak Djokovic recovered from a slow start as he continued the bid to retain his world number one ranking with a 4-6, 6-2, 6-3 win over 14th-seeded Bulgarian Grigor Dimitrov in the Paris Masters third round.
Rafael Nadal, who lost all four of his previous Miami Open finals, will be out to snap a run of three straight defeats against Roger Federer.
A season that produced the biggest shake-up in men's tennis for more than a decade draws to a close next week with three ATP World Tour Finals debutants striving to sign off breakthrough years with a large exclamation mark.
Here is a timeline of Djokovic's decline since the last of his 12 Grand Slam titles.
Rafael Nadal is confident he will be ready to compete in this week's Miami Open despite turning his ankle in practice, the second seeded Spaniard said on Tuesday.
India's top singles player Somdev Devvarman was on Saturday drawn to a play a qualifier while wild cards Yuki Bhambri and Jeeven Nedunchehziyan will have to fight it out with top-100 players in their first rounds at the Aircel Chennai Open.
World number five Roger Federer delivered a tennis masterclass to beat rising star Alexander Zverev 6-1, 6-3 and clinch a record ninth Halle Open title on Sunday as he lay down a marker in the lead-up to Wimbledon.
Grigor Dimitrov reached his first grand slam quarter-final in over two years on Monday by defeating an injury-hampered Denis Istomin 2-6, 7-6(2), 6-2, 6-1 to end the Uzbek wildcard's fairytale run at the Australian Open.
After six months out of the game, Federer's fairytale return continued under the lights of Rod Laver Arena where he emphatically quashed doubts about his fitness in three hours and 24 minutes of high-octane tennis.
It was a day of surprises at Flushing Meadows in New York as seeded players were knocked out one after the other on Friday.
Former world number one Rafael Nadal displayed more signs of a return to top form with a ruthless 6-2, 6-1 hammering of Stanislas Wawrinka to reach the semi-finals of the Shanghai Masters on Friday.
World No 1 Novak Djokovic recovered from another slow start to beat Spain's David Ferrer.
The triple grand slam winner, who will take over from Serb Novak Djokovic at the top when the rankings are updated on Monday, still went out on centre court for a practice session in front of a bemused crowd.
With three of the four Grand Slam titles and a record six Masters Series crowns scooped up in a year of domination, Novak Djokovic could be forgiven for using the ATP Tour Finals in London as a well-earned lap of honour.
Check out some of the up-and-comers who could cause an upset at Wimbledon this year.
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