Kyrgios broke British hearts when he cut short Andy Murray’s comeback in the opening round by winning a thrilling three-set tie.
And he continued his fine form against Edmund to set up a quarter-final clash with reigning champion Feliciano Lopez.
Kyrgios and Edmund held serve for the duration of the tight first set as they raced to a tiebreak inside 33 minutes.
Aces were aplenty as Edmund only lost five points on serve throughout the set, while Kyrgios gave away just four.
But it was the Australian who got the mini-break early in the decider before he went on to win 7-6.
Kyrgios said he had arrived in west London ready to entertain but he was much more professional, as he needed to be, to take the first set.
But with the advantage, he began to spread his wings in the first game of the second set and drew gasps from the crowd with a stunning tweener close to the net.
Kyrgios earned the first break point of the match in the same game but Edmund defended it well.
It took until the ninth game of the second set for Kyrgios to receive another break point with the score at 4-4, but again Edmund was resolute.
The world No 21’s return grew stronger throughout the match and he wasted another two break points in the 11th game – lashing a wild backhand wide across court to spur a 15-40 lead.
Kyrgios shook his head as he returned to his chair 5-6 down in the second set, frustrated to have passed up four golden opportunities.
But he came out to take the set to another tiebreak with strong service game.
Edmund stormed to a 4-0 lead in the tiebreak but Kygrios pulled his two mini-break deficit back, before the Brit took the set.
Kyrgios produced a moment of magic in the second game of the deciding set with an outrageous tweener lob.
And he went on to get the first break of the match in the fourth game as Edmund slammed a forehand wide.
The duo continued to hold serve as Kyrgios claimed another thoroughly entertaining victory with his third match point.