The 28-year-old from Stockport was knocked out of the singles in the second round by Hungary's Timea Babos, who lost to world number three Garbine Muguruza in the final.
But Broady responded in style by taking the doubles title along with Tormo as they beat Mexico's Giuliana Olmos and Desirae Krawczyk of the USA 3-6 6-4 10-8.
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The world number 134, who will be looking to make a big impression in the grass-court season, was clearly buoyed by her first WTA title.
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