Fourth seed Hsieh failed to book a quarter-final berth after coming off the worse in a two-hour battle with Japan's Misaki Doi.
The world number 38 looked to have recovered her composure after losing the first set but instead slumped to a 6-4 4-6 7-6 (7/3) defeat.
Next up for Doi is Italian qualifier Flavia Pennetta, who kept Maria-Teresa Torro-Flor of Spain at arm's length to ride out a 6-2 6-3 victory.
Razzano of France saw off number-two seed Tamira Paszek in Tuesday's opening round but could not outplay Johanna Larsson, who won 6-3 6-3.
Nimes-born Razzano brought a reputation as a giant-killer to Strasbourg having stunned 15-time Grand Slam winner Serena Williams in the first round of last year's French Open.
Sweden's Larsson will now face right-hander Lucie Hradecka after the Czech ousted American Lauren Davis 6-2 6-2.
Third seed and new home favourite Alize Cornet - last year's runner-up - survives after beating Poland's Magda Linette 6-3 6-4 to set up a match against seventh seed Chanelle Scheepers.
The South African recovered from a set down to beat American Shelby Rogers 2-6 6-3 6-4 in less than two hours.
Elsewhere, fifth seed Monica Niculescu of Romania fell to a 4-6 6-3 6-2 loss to Anna Tatishvili.
The Georgian's reward is a last-eight encounter with Canada's Eugenie Bouchard, who made light work of 21-year-old Camila Giorgi in a 6-3 6-0 win.
The Miami-based Italian might have expected to do better having dismissed top seed and 2011 finalist Marion Bartoli in straight sets on Tuesday.