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The 25th seed overcame a wobble in the second set to eventually progress by a 6-3 6(2)-7 6-3 scoreline, her first win over the distance since January.
Bouchard has suffered a dramatic fall from grace during 2015, with her opening-round win over Alison Riske just her 10th success of the year, a run that leaves her outside the top 50 for this season.
The former Wimbledon finalist started poorly against Hercog as she lost her opening service game, but she roared back to break her opponent twice on the way to taking the first set.
The second set went back and forth, but Bouchard gave herself a chance to serve for the match at 5-4, only to see Hercog deny her victory before controlling a second-set tie-break to take the contest into a decider.
Bouchard regrouped and gained control of the third set, and although she squandered two match points when serving for the match for a second time, she made no mistake with the third to move through to a showdown with Dominika Cibulkova.