The Bulgarian, who struggled with an ankle injury towards the end of last season, saved six out of seven break points to down his unseeded opponent in the season-opening tournament.
"I felt I was actually hitting the ball quite all right for our first match of the year," former world number three Dimitrov, who has slipped to 19th in the rankings, said.
Up next for the 2017 champion is Australia's John Millman or American Tennys Sandgren.
The big-serving Milos Raonic, another former world number three who slid down the rankings last season to sit one place above Dimitrov, fired 18 aces in his 6-0 6-3 win over Slovenia's Aljaz Bedene.
Canadian Raonic, the 2016 winner in Brisbane, next takes on qualifier Miomir Kecmanovic.
Among the women, 2017 winner Karolina Pliskova rallied from a set and a break down to beat Yulia Putintseva 4-6 6-3 6-4.
Wildcard Kimberly Birrell fought back from 3-5 down in the decider to stun Russia's world number 10 Daria Kasatkina 5-7 6-4 7-6(3) for her first win over a top-10 player.
Fellow Australian Destanee Aiava produced another upset, beating Kristina Mladenovic 6-3 7-6(2) to set up a second round clash with U.S. Open champion Naomi Osaka.
