Kyrgios, who beat Britain's Andy Murray in the first round, won 7-6 (7-3) 6-7 (5-7) 6-3 against seventh seed Edmund.

He will be joined in the quarter-finals by Novak Djokovic, who beat second seed Grigor Dimitrov 6-4 6-1.

Serbian 12-time Grand Slam champion Djokovic, a wildcard at Queen's after injuries, won in just over an hour.

'No logic' to Kyrgios game

Australian Kyrgios, 23, was at his unpredictable best against Edmund, playing 'hot dog' shots through his legs and delivering 135mph second serves.

Edmund, who had been the only Briton left in the tournament, levelled the match with a roar when Kyrgios' shot went long in the second-set tie-break.

But in the next game Kyrgios resumed his unconventional tennis, lobbing Edmund with a shot between his legs, which had BBC commentator John Lloyd exclaiming: "That is insane. There is no logic to that shot at all.

"To go for the lob from that position... that's one of the most inventive shots I've ever seen. How can you get away with that?"

Kyrgios broke in the fourth game of the third set and, despite looking increasingly uncomfortable with a hip problem, held on to serve out the match, sealing victory with a backhand down the line.

Nick Kyrgios (left) has beaten two Britons at Queen's this year - first Andy Murray and now Kyle Edmund

Kyrgios, who has been fined over his behaviour in the past, became frustrated towards the end of the match and was heard swearing towards his player's box.

Asked by a reporter about his outburst, he said: "Do you swear? No, do you swear? Yes or no? Yes or no? Do you swear? Do you swear?"

Kyrgios faces 2017 champion Feliciano Lopez in the quarter-finals.

"I knew today was going to be tough," Kyrgios, who served 32 aces to Edmund's 11, told BBC Sport.

"Kyle's had a great year. He's got a lot of firepower. It was a great battle.

"I haven't played too many matches in the past couple of months. Serving for a match of this value is not easy and I'm happy to get through it."

The players met again later on Thursday, with Edmund and Neal Skupski beating Kyrgios and compatriot Lleyton Hewitt 6-1 6-4 in the doubles.

Djokovic breezes past off-colour Dimitrov

Djokovic registered his first win over a top-10 player since May 2017 with a speedy victory over Dimitrov.

Bulgarian Dimitrov struggled for rhythm and won only 54% of points on his first serve.

He served five double-faults, one of which allowed Djokovic to close out the opening set, and created only one break point opportunity.

While it was not always easy for Djokovic - he double-faulted three times in attempting to close out the match - he targeted Dimitrov's backhand as he registered his 799th career win.

"Grigor made some crucial double faults today that handed me the first set," Djokovic told BBC Sport.

"He loves playing on grass. He's a great quality player."

Djokovic will face Adrian Mannarino in Friday's quarter-finals after the Frenchman beat compatriot Julien Benneteau 7-6 (7-4) 6-3.