Watson, who captured the Prague Challenger title last week, raced into a 3-0 lead in the first set but a lapse in concentration saw that advantage cut to 3-2.
However, the young Brit broke back to give herself a 4-2 advantage before the rest of the set went with serve.
Watson began the next set with another break but Zahlavova Strycova again managed to break back to level things up at 2-2
However, the British number two again secured a break – this time in the seventh game of the set – before seeing out the set to move into the next round.
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