Roger Federer annihilated Andy Murray 6-0 6-1 to seal top spot in Group B in London.
Novak Djokovic defeated Stan Wawrinka 6-3 6-0.
Czech returns with a win after losing first match at ATP finals in each of the last five editions.
Djokovic is seeking a 3rd consecutive title alongside the River Thames, one that would seal the world no.1 ranking.
Kvitova will attempt to overcome a losing record against Petkovic of Germany to give the Czech Republic a good start.
Swiss master has a chance to cap off a good year by reclaiming the No.1 ranking at the ATP World Tour Finals.
Murray will take on World No.1 Novak Djokovic for a semifinal spot after the Serbian beat Frenchman Gael Monfils.
Djokovic, who is in a race with Federer to end the season on top, quickly build the lead playing some aggressive tennis.
In Paris, Federer and Djokovic will battle it out this month to claim the world number one spot.
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.
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.