Edmund struggled with his serve right from the start of the match but managed to save five out of six break points to overcome his opponent in two hours and 30 minutes.
"Everyone wants to start well but the year is so long that if there's positivity you feel good but even if you don't start well it doesn't mean the year is going to be a bad one," the Briton said.
"It's always good to come to Brisbane, I made the quarters last year, got a good win this year so it's definitely helped my game going into the year."
ATP Brisbane
Sealed with an ace - Kyrgios takes Brisbane title in impressive fashion
07/01/2018 AT 10:58
Edmund next plays Chung Hyeon after the South Korean world number 58 withstood a barrage of booming serves from fifth seed Gilles Muller before winning 6-3 7-6(1).
Earlier, former world number one Andy Murray's lingering hip issues forced him to withdraw from the event with the Briton admitting he was unsure whether he could recover in time for the Australian Open later this month.
American Michael Mmoh won his first match on the ATP Tour after seven previous defeats, with a clinical 6-3 6-4 victory over Federico Delbonis. The teenager takes on eighth seed Mischa Zverev in his next match.
Denis Istomin had to dig deep to stun seventh seed Damir Dzumhur, winning 6-7(4), 6-3, 6-2 in two hours and 24 minutes.
ATP Brisbane
Kyrgios gets Brisbane title boost ahead of Australian Open
07/01/2018 AT 10:52