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Patty Schnyder had straight-set win against Ana on Tuesday to reach the second round of the Porsche Grand Prix.
Schnyder converted her fourth match point to beat Serbia-Montenegro's Ivanovic, who has risen from 97th to 18th in the rankings this year, in 53 minutes.
Known for her aggressive style, Ivanovic made twice as many unforced errors (26-13) as her opponent and often followed a volleyed winner with an easy miss.
"I expected it to be tougher against her," Schnyder said. "But a few missed shots and losses of serve and it can go pretty fast out there. This was a tough first-round opponent."
Ivanovic, who rose a last-year record 608 ranking spots, won her first title at Canberra in January. She then beat Amelie Mauresmo at the French Open en route to the quarterfinals.