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The 34-year-old American took her one and only break point in the first set to go 5-4 in front before serving out the opener to love on No. 2 Court.
The second was also evenly contested, but this time it was Spain's Torro-Flor who snatched the only break to clinch the set 6-4 and level the match.
The first four games of the decider were shared before Williams reeled off four in a row to win through 6-4 6-4 6-2 and book her place in round two.
Williams, seeded 30 at this year's tournament, will next play Japan's Kurumi Nara on Wednesday.