The German won the first set 6-3 before Troicki claimed the second 3-6. However, Zverev was victorious by the third and final set 6-4.
Simon, former world No.6, was rarely troubled during his first round encounter with wildcard entry Gulbis and he comfortably defeated the Latvian 6-3, 6-3.
The 32-year-old was joined in the second round by compatriot Richard Gasquet, who was equally emphatic in his opening match, taking just 66 minutes to dispatch experienced Spaniard Feliciano Lopez 6-2, 6-3.
Herbert beat Bernard Tomic 7-6 (3), 7-5 in a close battle and his victory over the Australian also ended the six-match losing streak he was previously on.