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The American found it easy to hit winners past her opponent, and wrapped up her first set in less than half an hour, winning every single one of her points on her first serve.
But the Spaniard mixed up her game in the second set, breaking the Stephens serve and recovering from 0-3 down to lead 4-3.
Highlights: Erratic Stephens progresses
Then Stephens promptly broke to love twice in a row, but struggled to hold her own serve.
Sorribes Tormo double-faulted twice when serving out the second set, and it ended up in a tie-break - and the seventh seed's big-match experience made the difference.
Meanwhile, 2016 Roland Garros champion Garbine Muguruza enjoyed a straightforward victory of her own, beating Sweden's Johanna Larsson 6-4, 6-1 to set up a third-round clash with Elina Svitolina.
Sir Bradley Wiggins & Lizzie Deignan