Williams, runner-up to Jana Novotna in the Faber Grand Prix last week, is ranked No 5 in the world and is top seed in the event she won a year ago.
The third seed, Amanda Coetzer of South Africa, romped past Elena Wagner, of Germany, 6-1, 6-3.
Lilia Osterloh, a qualifier ranked 119th, continued to advance with a 6-4, 6-3 win over Japan's Miho Saeki. Cara Black, of Zimbabwe, also made it into the quarter-finals by beating France's Alexia Dechaume-Ballert 7-6, 7-6.
Williams hit a 116mph ace on the first point of her match and needed just 22 minutes to take the first set, 6-1. The second set was a struggle for Williams as Po broke her serve once and took advantage of five double faults, three of them in the final game that forced the tie-breaker.
"I thought I was going to set a record in the first set," Po said. "I didn't even see her first serve. I had never played her and it took a while for me to adjust. Her movement is a big weapon. She is tall and most players that big don't move well."
Williams, who meets Alexandra Stevenson in the quarter-finals, was pleased with the win. "Kim hits the ball flat and low and that is out of my [strike] zone." Williams is the only seeded player left in her side of the draw while Coetzer, the second seed, Anna Kournikova, and fifth seeded Chanda Rubin are all in the other half.
Venus and her sister Serena were among 10 players selected to the US Fed Cup team by captain Billie-Jean King. Lindsay Davenport will play in the first-round Fed Cup match against Croatia on 17 and 18 April.Reuse content