The Russian won on her third match point when Ivanovic, who took a medical timeout in the first set, hit a forehand into the net.
The WTA said Ivanovic, the French Open champion, had a virus.
The ninth-ranked Zvonareva has won two White Group matches. Ivanovic has lost two. They have one more round-robin match.
The eight players are divided into two round-robin groups, with the two leaders of each going into an elimination stage.
Later Wednesday, Venus Williams played Elena Dementieva and Serena Williams faced Dinara Safina in Maroon Group play.
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