Sharapova and Radwanska claimed wins in White Group round-robin play while Williams is 1-0 after the only Red Group match Tuesday.
Williams, seeded third in the tournament, piled up five breaks in a 6-4, 6-1 win over fifth-seeded Angelique Kerber. Williams lost her serve once early but ended up winning 72 percent of the points on serve and nearly as many -- 30-31 -- of the points as Kerber when receiving serve. Williams has won 27 of her last 28 matches.
Sharapova, No. 2 in the world, finished Tuesday's schedule with a 6-3, 6-2 decision over seventh-seeded Sara Errani. It was the same score Sharapova posted in beating Errani in the finals of the French Open.
Errani broke Sharapova's serve for a 2-0 lead in the first set but Sharapova controlled things from there. She had a pair of breaks in each set and dropped only 17 points -- four in the second set -- in nine games serving.
The fourth-seeded Radwanska handed defending champion Petra Kvitova a 6-3, 6-2 setback. Radwanska won 58 percent of the points serving and 59 when receiving serve and backed a pair of breaks in the first set with four in the second.
Kvitova saw a 25-match winning streak on hard courts snapped.
Round-robin play continues Wednesday with Williams taking on eighth-seeded Li Na and world No. 1 Victoria Azarenka playing Kerber in the Red Group while Sharapova goes against Radwanska in the White Group match.