The 23-year-old Kuznetsova raced to a 4-0 lead in the first set Sunday before Medina Garrigues could find a response to her powerful ground strokes. The Spanish player broke back three times to take a 6-5 lead and served out the set in clear sunny conditions at Club de Campo Villa de Madrid's clay court.
"It's an amazing feeling,'' Kuznetsova said. "Even though I wasn't playing my best game it's so important for me to win this point for the team.''
The players then traded breaks to reach 3-3 in the second, before Kuznetsova won three straight games to level the match and then got a late break in the third to secure the win that gave Russia an unbeatable 3-0 lead.
"She's a player who puts great weight on her deliveries,'' Medina Garrigues said. "I gave it my all.''
Kuznetsova was worried when Medina Garrigues kept fighting back, but knew her superior stamina would be a factor.
"I gave her a chance to get back,'' she said. "I started to play a little bit of baseline tennis against her game. (But) I felt so much more energy, I knew my fitness was better.''
Russia extended its lead to 4-0 when Elena Vesnina and Ekaterina Makarova beat Nuria Llagostera Vives and Carla Suarez Navarro 6-2, 6-1 in the doubles.
On Saturday, Vera Zvonareva beat Medina Garrigues, while Kuznetsova defeated Spain's Carla Suarez Navarro.
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