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The Belgian lost both matches at the inaugural United Cup last week, but he saw off Bublik 6-3 6-4 in 74 minutes to reach the last 16 in New Zealand.
Another seeded player fell at the first hurdle on Monday as Adrian Mannarino lost 6-4 7-6 (7-4) to J.J. Wolf.
Richard Gasquet advanced with a 6-3 6-1 win over wild card Kiranpal Pannu, while Jenson Brooksby beat Fabio Fognini 6-7 (2-7) 6-1 6-3 and will now face Diego Schwartzman.
At the Adelaide International 2, fifth seed Dan Evans suffered a 7-5 7-5 defeat to Mackenzie McDonald.
Fellow seeds Alejandro Davidovich Fokina and Miomir Kecmanovic overcame Brandon Nakashima and Kyle Edmund respectively.
