Murray will take on World No.1 Novak Djokovic for a semifinal spot after the Serbian beat Frenchman Gael Monfils.
Murray's clinical 6-3, 6-3 win over Grigor Dimitrov guaranteed him a berth at the O2 Arena from Nov. 9-16.
Djokovic, who is in a race with Federer to end the season on top, quickly build the lead playing some aggressive tennis.
Murray will lead Manila Mavericks in Mahesh Bhupathi's league, starting November 28 in Philippines.
Sania expressed happiness over Prime Minister Narendra Modi wishing her after the WTA Finals triumph.
Wozniacki decided to run the New York Marathon after golfer Rory McIlroy called off their wedding.
Murray, meanwhile, believes Gala Leon's appointment as Spain's Davis Cup captain was handled “horribly”.
In Paris, Federer and Djokovic will battle it out this month to claim the world number one spot.
The 17-times grand slam champion edged out David Goffin 6-2 6-2 to win the Swiss Indoor tournament for the sixth time.
Sania was quick to thank PM, saying, "@narendramodi Thank you very much Sir..humbled by your wishes."
Murray saved two match points in the second set and three in the third before winning 3-6, 7-6 (7), 7-6 (8).
The win will ensure Williams extends her stay at number one in the rankings to 97 weeks.
Serena Williams avenged her "embarrassing" loss to Simona Halep in the group stage with a ruthless display.
Sania and Cara beat Su-Wei Hseih of Chinese Taipei and Shuai Peng of China 6-1, 6-0 in straight sets.
The world number one Williams will take on Simona Halep in Sunday’s final.
Top-seeded Roger Federer beat the big-serving Croat Ivo Karlovic 7-6 (8), 3-6, 6-3.
Wozniacki served for the match at 5-4 in 3rd set but Serena broke back and won the tiebreaker and match.
The Spaniard also needed treatment for appendicitis this month in Shanghai.
Serena Williams takes the year-end top ranking for the fourth time, beside she achieved the feat in 2002, 2009 and 2013.
Sharapova needed to win in straight sets to stand any chance of advancing to the semi-finals.
It was the American’s worst loss since her defeat by Kruger in the quarter-finals at Oklahoma City in 1998.
Halep took Serena back 16 years to a time when, as a teenager, she was trying to make a name for herself.
Nadal notches up no nonsense 6-2, 6-2 win over Simone Bolelli in Swiss Indoors on Monday.
The Dane grabbed the final qualifying spot but it was Sharapova who looked the lower ranked player.
Serena Williams puts aside storm over disparaging comments by ITF member to beat Ivanovic 6-4, 6-4.
Serena begins her WTA Finals title defence with a 6-4, 6-4 win over Ana Ivanovic in Singapore.
The WTA took swift action and fined Tarpishchev $25,000 and disqualified him from working in an organisational capacity.
The victory also boosted Murray’s chances of getting to the eight-man ATP finals in London next month.
Tarpishchev made an official apology on Saturday after a WTA demand to do so.
Tarpischev was fined and suspended for a year after referring to Serena and Venus Williams as “brothers’’.
The tour also said Tarpischev owes Venus and Serena Williams a personal apology.
The league, brainchild of Bhupathi, will begin on Nov 28 in Singapore and conclude on Dec 13 in UAE.
Soderling attained a career high ranking of No. 4 before he was struck by mononucleosis, which laid him low for months.
The 17-time Grand Slam singles champion won 7-6 (6) 7-6 (2) to register his first title in China.
Federer triumphed 7-6 (6) 7-6 (2) to register his 23rd Masters Series title and first in China.
Roger Federer ends Novak Djokovic’s unbeaten 28-match run in China; sets up date with unseeded Simon.