Cilic last beat Nadal nearly a decade ago, in Beijing, 2009, losing their next five.
This Melbourne edition will be the first since 2007 when at least two of the big four -- Roger Federer, Nadal, Novak Djokovic and Andy Murray -- were not a part of the semifinals.
Edmund's elimination of Dimitrov came with the Brit carrying the weight of his nation after Murray was forced to miss the major following knee surgery.
No. 49 Edmund is only the sixth British man to reach a Grand Slam semi since Open tennis began in 1968. One of that number, Tim Henman, was in the stands watching the upset.
"You don't think about records when you are playing," Edmund said. "But it's something to be proud of."
Edmund surprised Dimitrov by winning the opening set and did not falter when he then lost the second before gunning his jets over the next two sets to earn the win.
Edmund won in two hours 49 minutes, striking 46 winners and sending over 13 aces.
In the women's draw, Belgium's Elise Mertens continued her golden tournament debut defeating injured fourth seed Elina Svitolina 6-4, 6-0 to earn the first of the semifinal spots.
She will face 2011 semifinalist Caroline Wozniacki after the second seed fought through in the early morning hours to beat Carla Suarez Navarro 6-0, 6-7 (3-7), 6-2.
The 22-year-old Mertens, who trains at the academy of former Belgian great Kim Clijsters, was hoping that her mentor might have been up in the early hours back home, watching the quarter-final showdown.
Svitolina, from Ukraine, was tipped as a title favorite and had been in the running for a shot at the WTA number one title before she fell victim to Mertens.
She later revealed that she has been dealing with a left hip injury throughout the event, managing to play only with the help of painkillers.
Victory for 39th-ranked Mertens took 73 minutes and featured 26 winners and five breaks of serve.
The last Belgian to get this far at the Australian Open was Clijsters in 2013, a year after winning the trophy.
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