Dimitrov was the first to come to his aid, leaping the net and sprinting over to help his opponent up and guide him to his chair.
The deciding set was equally close with Edmund saving two break points in his opening service game but he was unable to seal a first win in 14 attempts over a top-10 ranked player.
"I thought I was out - he pushed me to the limit, " Dimitrov said.
Earlier Friday, Kyrgios had his left knee heavily taped but didn't appear to be hampered as he worked his way into the match after dropping the first set in 22 minutes.
After Dimitrov got the best of Edmund during a rally, Edmund went down, holding his ankle in agony. "It's very unfortunate what happened, for sure".
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"I'm feeling pretty good".
The other semi-final will feature another Australian, 18-year-old Alex De Minaur, and unseeded American Ryan Harrison - who had been due to play Murray on Thursday before the Briton withdrew from the tournament.
"I will look to fly to Sydney and I'm ready to pick myself up and go again, " he said. I'm hitting the ball well and I'm serving really well.
Dimitrov will face Australia's Nick Kyrgios in the semi-final after he overcame Ukraine's Alexandr Dolgopolov 1-6 6-3 6-4. The 18-year-old de Minaur stunned fourth seed Milos Raonic in the second round and there was no letdown Friday as he ousted United States qualifier Michael Mmoh 6-4, 6-0 to reach his first ATP semi-final.
In the women's draw, Svitolina upset second seed Karolina Pliskova, winning 7-5, 7-5.