Unseeded Venus Williams marched into the Family Circle Cup semi-finals by beating Spain's Anabel Medina Garrigues 6-4 7-5 on Friday.
The American ace beat Vera Zvonareva while US Open champion Kuznetsova accounted for Wimbledon champion Maria Sharapova in the semi-finals of the China Open.
Vera Zvonareva sent world number one Maria Sharapova to a stunning 4-6, 7-5, 6-1 at the Pacific Life Open.
Elena Dementieva made a confident start to her claycourt campaign as she beat compatriot Alina Jidkova 6-4, 6-4
Unheralded Igor Kunitsyn upset former world number one Marat Safin 7-6, 6-7, 6-3 in an all-Russian Kremlin Cup final to clinch his maiden title.
Mary Pierce edged Vera Zvonareva 6-4, 3-6, 6-3 to send France into the Fed Cup final against the United States.
The sixth seeds needed a little over an hour to overcome the unseeded pairing of Roman Safiullin of Russia and Kazakhstan's Andrey Golubev 6-3, 6-3 in a second round match.
Vera Zvonareva of Russia beat India's Sania Mirza 7-5, 6-1 to win the Pattaya Open on Sunday.
World number two Rafael Nadal dropped a set at the Barcelona Open for the first time in four years before advancing to the last 16, beating Argentine Leonardo Mayer 6-7(7), 6-4, 6-2 on Wednesday.
Novak Djokovic took a first unsteady step toward completing the calendar-year Grand Slam on Tuesday as the Serb laboured into the second round of the US Open with a 6-1, 6-7(5), 6-2, 6-1 win over dashing Danish teenager Holger Rune.
At one stage Yuki was a break up, serving for the opening set but lost his serve and eventually the set. After drawing parity, Yuki twice lost his serve to fall behind 0-3 in the decisive set and never recovered.
Summary of sports events and persons who made news on Saturday
The tension mounted and temperatures soared at the U.S. Open as top seed Novak Djokovic and Andy Murray set up a sensational quarter-final, and Serena Williams made a 2014 grand slam breakthrough.
Images from matches played on Day 4 at the US Open at the Flushing Meadows in New York on Thursday.
Images from Day 2 of the 2020 US Open in New York
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