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.
The Dane grabbed the final qualifying spot but it was Sharapova who looked the lower ranked player.
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.
Roger Federer ends Novak Djokovic’s unbeaten 28-match run in China; sets up date with unseeded Simon.
Djokovic sets up semifinal against Roger Federer after thrashing Ferrer; Simon upsets Thomas Berdych.
Suffering from appendicitis, Rafael Nadal succumbs to Feliciano Lopez; Roger Federer stages comeback.
Nadal said on Tuesday he chose to try treatment with antibiotics rather than undergo surgery right away.
The 27-year-old Serb took an hour and 37 minutes to down Murray for an impressive 23-0 record in Beijing.
Gala Leon became the first woman to be appointed captain of the country’s Davis Cup team on Sunday,
She hasn’t played since a third-round defeat at Wimbledon, withdrawing from the U.S. Open citing a knee injury.