Evans needed just 75 minutes to beat Kazakhstan's Bublik 7-5 6-2.

The Briton, who will be seeded at a Grand Slam for the first time when the Australian Open begins on 20 January, will face either Russia's Andrey Rublev or American Sam Querrey next.

Elsewhere, Britain's Kyle Edmund claimed his first victory of the year at the Auckland Open.

Edmund, who has slipped to 67 in the world rankings, beat Spain's Alejandro Davidovich 6-2 4-6 6-3.

He will play either Italy's Andreas Seppi or French seventh seed Adrian Mannarino in the second round.