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Having eased through a one-sided opening set in 34 minutes, Errani lost her way at the start of the second, falling a double break behind. However, the Italian, never one for giving up on lost causes, was not done and was rewarded for her persistence when she clawed back one of the breaks.
The second soon followed, thanks to a delightfully disguised drop shot, and with it the momentum as Koukalova started to become increasingly frustrated with Errani's tireless retrieving. Two games later, the comeback was complete, Errani wrapping up a 63 64 victory when a forehand from the Czech flew long.
"I like to play drop shots from time to time," Errani said when asked about her shot selection on the break back point in the second set. "It's good to mix things up sometimes and surprise your opponent. When you are running from side to side, it is often difficult to come forward and reach a short ball when you don't expect it.
"I've played a lot of matches and practices and I've always liked this shot. I like to practice sometimes by playing small court games and this improves your hands, improves your touch and helps when you need to play a shot like this at an important moment."
Despite all her success on the clay down the years, highlighted by six WTA titles and a French Open final on the surface, this was Errani's first main draw win in five visits to Stuttgart.
Her reward for breaking this duck is a second round meeting with the big hitting Kaia Kanepi, who booked her place with a hard-fought win on Monday over lucky loser Johanna Konta.