The enigmatic Australian defeated Kazakhstan's Andrey Golubev 6-4, 6-4 at the tournament in England's south.
It was only his second ATP win since January and he will next face top-seeded Frenchman Richard Gasquet
"I think I served very well today and it's something I've worked on in the last few days so it's good to see it coming out in a match," Tomic said.
Meanwhile Jeremy Chardy showed impressive resolve to knock fifth seed Ivo Karlovic out.
Big-serving Croat Karlovic fired down 14 aces, but also committed eight double faults, with Chardy jumping over his second serve en route to a 6-4 6-4 victory.
Chardy managed to return 19 of Karlovic's second serves, winning points on 15 of those occasions.
The Frenchman - ranked 43rd in the world - was supreme on his own serve, conceding just nine points in the entire contest as the two-time winner of the ATP 250 grass-court event wilted.
Victory was Chardy's first of the grass-court season
A further shock in Monday's play at Eastbourne saw eighth seed Federico Delbonis beaten 6-4 6-4 by Martin Klizan.
Delbonis came into the game having suffered first-round defeats in three of his last four tournaments and he continued that dismal run, failing to carve out a single break point in the 70-minute contest.
Sixth seed Gilles Simon avoided an upset against Australian qualifier Chris Guccione, triumphing 7-6 (7-2) 6-4.
Defending champion Feliciano Lopez will begin his title defence against Tobias Kamke after the German beat Britain's Daniel Evans 6-2 6-3, while home fans also had little to cheer about in Sam Querrey's 7-6 (7-5) 6-3 win over Kyle Edmund.
Also booking a spot in the second round in Monday's play were Denis Istomin and Carlos Berlocq.