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Tomic, at 19 the youngest man in the field in the Catalan capital, spent 67 minutes in handing one-time prodigy Gulbis another ATP disappointment.
The two-time quarter-finalist Latvian who has faded to an 86th ranking after standing a career-best 21st just 14 months ago, went down on two breaks of serve.
Tomic, who won a round in Monte Carlo last week but lost his next match to Ukrainian talent Alexandr Dolgopolov, was pleased with a winning start in the hotbed of Spanish tennis.
"I played well from the first game," said the Australian 15th seed. "I was able to play my game.
"I served well and got more comfortable on the clay," added the number 35, the youngest man in the field. "I'm moving better and feeling better. I'm playing well right now."
Tomic faces a big test in the next round as he takes on Spanish clay-courter Alberto Montanes, winner of five titles on the surface.
"He gets a lot of balls back, it will be a different match," said Tomic, who improved to 14-7 on the season. "I've got to be ready to be physical and aggressive with him. And I've got to play much more patient."
Tomic's haul of 14 victories since the start of 2012 puts him to within two of his total of 16 for 2011.
South African 13th seed Kevin Anderson posted a quick win over outclassed Tunisian Malek Jaziri 6-2, 6-3, with the winner saving six break points.
Second seed Andy Murray was making his start after a bye as he faced Sergiy Stakhovsky of the Ukraine while top seed and six-time winner Rafael Nadal was due to play his first match on Wednesday.
