Defending champion Patty Schnyder also reached the last eight by upsetting third seed Amelie Mauresmo 6-2, 6-2.
Leading Russians, third seed Anastasia Myskina and fourth seed Nadia Petrova, tumbled out in the Rome Masters.
It was the Frenchwoman's second title in as many weeks and her fifth this year, improving her record to 5-0 against Zvonareva.
New world number one Amelie Mauresmo struggled to a 7-5, 6-4 victory over Patty Schnyder in the second round of the Filderstadt Grand Prix.
The second seed advanced to the quarter-finals of the $1.3 million Montreal Cup with a 6-2, 3-6, 6-2 over Elena Bovina of Russia.
Mauresmo overcame Paola Suarez while Serena thrashed Jennifer Capriati in the women's quarter-finals at Wimbledon.
The Slovak will meet Svetlana Kuznetsova in the final of the Eastbourne International.
The 22-year-old Moscovite beat Amelie Mauresmo in the final.
Jennifer Capriati stunned top seed Serena Williams 6-4, 6-4 in the semi-final of the Rome Masters.
The American reached the milestone after beating Amelie Mauresmo in the final of the Amelia Island tournament.
Amelie Mauresmo shocked the world number one 6-7, 7-5, 6-3 in the semi-finals of the Amelia Island championship.
Here are some of the best moments from the 2019 Australian Open.
The victory earned the Belgian a place in the final of the German Open.
The duo meet in the semi-finals of the German Open.
The French top seed beat the American 4-6, 7-5, 6-4 in the final of the Antwerp Diamond Games.
The world number two said she plans a more attacking approach for the last three Grand Slam events of the season.
Amelie Mauresmo crushed American Meghann Shaughnessy 6-2 6-1 on Sunday to power France to their second Fed Cup title.
Agassi polished off former world number one Yevgeny Kafelnikov 6-3, 7-6, 6-4 to reach the U.S. Open fourth round.
France's Amelie Mauresmo thrashed Elena Bovina 6-2, 6-0 to win her fourth title of the year at the $585,000 Linz Open on Sunday.
The Frenchwoman quashes claims that she is an unworthy world number one.
The world No. 1 joined Kim Clijsters, Justine Henin-Hardenne and Nadia Petrova in the semi-finals of the French Open.
Clijsters completed her inexorable progress to Sunday's final with a 6-3, 6-2 win over Sugiyama.
The unseeded Ostapenko, 20, downed Romanian third seed Simona Halep 4-6, 6-4, 6-3 in the final, hitting a staggering 54 winners and taking her tournament tally to 299.
The Belgian rallied from the brink of defeat to beat Amelie Mauresmo in the final of the Romes Masters.
Finally clinching an elusive Australian Open crown is Andy Murray's number one goal for the new year but the Briton concedes that his hopes of success at Melbourne Park may rest on champion Novak Djokovic having an off-day.
A few of the many, many, MANY faces of women we love, respect and desire.
Britain's Andy Murray has reunited with former coach Ivan Lendl as the World number two prepares for another tilt at the Wimbledon title.
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