Tomic, the fifth-seed at the ATP tournament in Germany enjoyed a 6-3 7-6 (7-5) win over Germany’s Jan-Lennard Struff.
The 22-year-old, who reached the quarter-finals of Wimbledon in 2011, converted three of his five break points for victory in 71 minutes.
“It’s very exciting for me to be back here,” said Tomic, who was born in Stuttgart before his family immigrated to Australia.??
“My first match on grass was pretty good. I served and returned well in the first set.
“It’s all about finding your movement on the grass in the first match and I felt like it was pretty solid.”
He will now face former world No 2 Tommy Haas of Germany in the second round.
Dominic Thiem and Lukas Rosol were the biggest-name casualties, the former being beaten 7-6 (7-4) 6-2 by Mischa Zverev and the latter going down 6-3 6-4 to Marcos Baghdatis.
Eighth-ranked Viktor Troicki saw off Borna Coric 6-2 6-0 while Jerzy Janowicz came from a set down to beat Dustin Brown 6-7 (7/5) 6-3 6-3 and Andreas Seppi got beyond Benjamin Becker for the loss of three games, 6-2 6-1.
Tommy Haas also progressed, beating Mikhail Kukushkin 6-4 7-5, while elsewhere there were victories for Andreas Haider-Maurer, Alexander Zverev, Sam Groth and Matthias Bachinger.
Fourteen-time Grand Slam winner Rafa Nadal will be looking to kick-start his season after dropping to 10th in the latest world rankings – his worst position in more than a decade.
Having lost to world No 1 Novak Djokovic in the quarter-finals of the French Open last week, it is the 29-year-old’s lowest ranking since reaching 11th as a teenager in April 2005.
Having had a bye to the second round, Nadal will play Baghdatis after the Cypriot beat Lukas Rosol 6-3 6-4 in their first-round clash with the 29-year-old looking to add to his lone win over Nadal from five years ago in Cincinnati.