Dimitrov was on court for nearly two-and-a-half hours before finally subduing the British number two, who was right in the contest until he hurt his ankle with the score at 4-4 in the third set.
Dimitrov jumped over the net from his side of the court and raced to help Edmund as he writhed in pain behind the baseline at the other end, giving the British player a hand to get up and then helping him limp to the side of the court.
Ranked 50th in the world, Edmund is looking to right the wrongs of last year's Australian Open when he suffered a straight sets second round defeat to Spaniard Pablo Carreno Busta.
Dimitrov saved both and in the next game the Bulgarian took advantage of a couple of errors to break for a 5-3 advantage, before serving out the set when Edmund netted a backhand. "It's very unfortunate what happened", Dimitrov said of Edmund's injury.
"The first match of the year and I get to play two-and-a-half hours", he said. That's just me, I guess.
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"I knew the last two games he wasn't at his best so I just had to find a way again", Dimitrov added.
"First match in about a month - I feel a little bit rusty, but at the same time I'm excited and trying to get into a rhythm".
Kyrgios had earlier battled back from a set down to beat Alexandr Dolgopolov 1-6 6-3 6-3 on Friday to book his spot in the semi-finals.
Teenage wild-card entry Alex De Minaur followed up his upset victory over Milos Raonic with a routine 6-4, 6-0 win over Michael Mmoh to reach his first tour-level semifinal.
The Brisbane born and raised Millman has played some of his best tennis on the Pat Rafter Arena, and has taken sets off Roger Federer and Andy Murray in previous tournaments. Harrison was leading 7-6 (6) 4-2 when Uzbekistan's Denis Istomin retired from the contest.