* Wozniacki training for New York marathon * Officials invoke heat rule stop match (Adds quotes, detail) By Steve Keating NEW YORK, Aug 31 (Reuters) – Denmark’s Caroline Wozniacki beat the heat and Maria Sharapova 6-4 2-6 6-2 to move into the quarter-finals of the U.S. The brutal conditions turned the match between Sharapova and the 10th seeded Wozniacki into a battle of survival, a fight the fifth seeded Russian could not win. Her departure leaves only top seed Serena Williams and Canadian seventh seed Eugenie Bouchard the only remaining members of the top eight still in action heading into the second week of the year’s final grand slam. “The depth of the women’s game now is so high,” said Wozniacki, who will next face 13th seed Sara Errani of Italy.