The Bulgarian, who is also the top seed at the tournament, broke Edmund in the eighth game of the first set to win 6-3.
Dimitrov came close to breaking Edmund in the ninth game of the second set, but the Briton defended two break points to stay in the match, and won the tie-breaker to live to fight in a deciding set.
Sealed with an ace - Kyrgios takes Brisbane title in impressive fashion
In the ninth game of the decider at 4-4, Edmund went down on his right ankle and Dimitrov leapt over the net to offer his competitor assistance.
Following a medical time-out, Edmund was able to play on but it was not long before Dimitrov broke the Brit’s serve to win the third set 6-4.
Dimitrov will play Nick Kyrgios in the semi-finals.
Kyrgios gets Brisbane title boost ahead of Australian Open