The Australian, whose outbursts have landed him in trouble here and elsewhere, secured the contest with his friend and occasional mentor by beating Feliciano Lopez 6-3, 6-7 (2), 6-3, 6-4 on Middle Sunday.
Kyrgios was actually pretty quiet by his standards as he produced an impressive and business-like finish to a match that started on Saturday evening.
He even said that the code violation he received at the last, on match point, for taking too long was "fair enough", but the pressure will really be on against Murray.
The Briton, another player prone to chatter away and berate himself and others during matches, is the favourite to take the title after Novak Djokovic's shocking exit.
Fireworks should be expected, and a key for both players' approaches will be how to stay calm and channel the tension and frustrations positively.
Murray, for one, indicated on Sunday he has found a way to deal with the increasingly intense spotlight on him.
"Ivan Lendl is a great person to have on the team when expectations start to build around me because he's been through the same experience himself, " Murray said in his BBC column.
"I remember that made it hard in terms of everyone focusing on me from early in the tournament, and I spoke with Ivan about it at the time, because it's an extra thing to deal with."
Murray noted that Kyrgios has beaten Nadal on Centre Court before, but he has a 4-0 record against the Australian and is 18-0 against players from Down Under.
Yet the 21-year-old's power -- in his serve and groundstrokes -- and ability to hit pancake flat shots have the potential to trouble the best.
Kyrgios was fined for his conduct in both of the previous rounds and, on Saturday night, was berating himself for being lazy and aiming offensive language at his players' box.
A day later he showed a maturity in the second installment of his match against Lopez that he hadn't shown at Wimbledon this year.
The 15th seed looked anything but lazy and even his full players' box -- who still stood to applauding attention at every opportunity -- were saved from the usual tongue-lashing.
On what is known by some as People's Sunday, he served well, played some stunning passing shots and did what some of the more sympathetic and experienced players on the tour think he will show more often when he matures: he won well without courting further controversy.
When asked in his postmatch BBC interview what pleased him most, Kyrgios said: "My attitude. It was tough after a darkness delay but I think my level of tennis was really high.
"Yes, I have the tools [to beat Murrray], but he is one of the best players in the world and he is probably the favourite now Novak is out.
"I'm going to go out there and not do anything different. We are great mates: he's a great guy, a great player and I'm going to go out there and enjoy it."