Thiem won 6-4 6-2 to register a second career victory over his good friend in an hour and nine minutes.
Latvia’s Gulbis, a semi-finalist in Holland last year, became the first seed to be sent packing from the tournament as world No 47 Thiem notched the upset.
The pair are both coached by Gunther Bresnik but that inside knowledge benefitted Thiem on the day, as he progressed past the first round for the second straight year.
Seventh seed Roberto Bautista Agut is also through to the second round after a straight sets win over Alexander Zverev.
Unseeded German Zverev kept pace for much of the first set until Bautista Agut cranked up the pressure to take a 6-4 6-1 win.
World No 50 Simone Bolelli of Italy strolled to a 6-3 6-1 win over World No 29 Lukas Rosol in the early part of Monday afternoon???s session.