0126 GMT November 24, 2017
Czech world number three Pliskova breezed past American Venus Williams 6-2, 6-2 in the opening round-robin match, BBC reported.
Wimbledon champion Muguruza of Spain then beat Latvia's French Open winner Jelena Ostapenko 6-3, 6-4 to join Pliskova at the top of the White Group.
The Red Group gets under way on Monday, with seven of the eight finalists able to finish the year as world number one.
Muguruza, who topped the rankings for three weeks this year, is 40 points behind current leader Simona Halep.
Neither Muguruza nor Ostapenko settled straight away in Singapore, with Muguruza eventually consolidating her break with a love hold.
Latvia's Ostapenko won their last encounter at the Wuhan Open in September but she struggled for consistency here.
Ostapenko hit 21 winners to Muguruza's 10, but her 25 unforced errors and four double faults cost her as she pushed Muguruza in the final few games.
She forced Muguruza to wait as the Spaniard served for the set, saving three match points, but Mugurza kept calm to secure victory.
Earlier Pliskova, who was world number one for seven weeks in the summer, sped past world number eight Williams in the first match of the day.
Williams, the oldest player at this year's tournament at 37, has appeared five times at the end of season event and won the title in 2008.
The Wimbledon finalist struggled with her serve against Pliskova, hitting six double faults and making 19 unforced errors to Pliskova's 12.
However, Pliskova's consistency showed as she hit 25 winners, along with five aces, to register a speedy victory.