The 22-year-old took the first set 7-6 on a tie-breaker and was off to a flying start, breaking Chung's serve in the fist game and holding his own to go 2-0 up.
However, Chung fought back to level 3-3, before breaking Edmund in the final game to win the set 7-5.
Sealed with an ace - Kyrgios takes Brisbane title in impressive fashion
Heading into the decider, the pair went through the motions until Edmund broke to edge ahead 4-3, then held to consolidate his lead, appearing to hit his stride winning five points consecutively.
Edmund lost two match points, to squander a 40-15 lead and give Chung a way back into the match. But, at 5-4 up, Edmund made light work of Chung in what would be the final game, to win the deciding set 6-4.
Edmund will face Grigor Dimitrov in the quarter-finals after he beat Australia's John Millman 4-6, 7-6, 6-3 in an epic showdown.
Elsewhere in the competition, Uzbekistan's Denis Istomin saw off competition from USA's Jared Donaldson to win 7-6, 6-2, and will face Donaldson's compatriot Ryan Harrison, who beat Germany's Yannick Hanfmann 7-6, 6-4, 6-2 in the quarter finals.
Kyrgios gets Brisbane title boost ahead of Australian Open