MELBOURNE, Australia — Rafael Nadal left the muttering and the preening, the underarm serving and the ’tweening, to his younger, flashier opponent, Nick Kyrgios.

Surely, Nadal was content to collect the win in the latest installment of their rivalry.

The No. 1-ranked Nadal kept his thoughts to himself and limited his shot-making to the more traditional variety in an entertaining 6-3, 3-6, 7-6 (6), 7-6 (4) victory over home-crowd favorite Kyrgios on Monday to reach the Australian Open quarterfinals and get closer to a record-tying 20th Grand Slam title.

These two guys don’t like each other. But Nadal had nothing but nice things to say after improving his head-to-head record to 5-3 against Kyrgios.

“When he wants to play, when he is focused on what he’s doing, I think he’s a very important player for our sport,” Nadal said, “because he has a big talent and is one of these players that can be very, very interesting for the crowd.”

While Kyrgios was up to some of his usual trick shots and antics, what he never did was waver in his effort, something folks often accuse him of.

“Today,” Nadal said, “I think he played very serious, tried all the time his best.”

It certainly meant a lot to Kyrgios, who said: “I’m shattered to have lost tonight. These are the matches that I want to win the most.”

Here’s how the elevated stakes and tension affected both men: At 5-all in the pivotal third-set tiebreaker, Kyrgios double-faulted. That offered up a gift-wrapped set point. But Nadal failed to take advantage because he double-faulted right back.

Still, two points later, the 23rd-seeded Kyrgios put a forehand into the net, and the set was Nadal’s. Not long after, Kyrgios double-faulted again to get broken at love.

That put Nadal ahead 2-1 in the fourth, seemingly in charge.

“Against Nick,” Nadal would say afterward, “you are never (in) control.”

Sure enough, Nadal faltered while serving for the win at 5-4, double-faulting to create a pair of break points, the second of which Kyrgios converted with a jumping forehand and celebrated by throwing his head back and screaming. Spectators rose and roared and waved their Australian flags in support of the 24-year-old from Canberra.

“A scary game,” Nadal called it, acknowledging his nerves got to him.

But he regrouped and pulled the win out in the closing tiebreaker, which ended with Kyrgios putting a forehand into the net.

Sure, the cool, breezy conditions played to Nadal’s advantage and dulled Kyrgios’ power-based style. But there also was this: Nadal finished with more than twice as many winners as unforced errors, 64-27.

“I’d have to win a point three times to win a point,” Kyrgios said.

Kyrgios delivered 25 aces and some memorable moments — including walking out on court and warming up for the match in a No. 8 Lakers jersey to honor Kobe Bryant, the five-time NBA champion and 18-time All-Star who died in a helicopter crash Sunday at age 41.

A video tribute to Bryant was played on the Rod Laver Arena scoreboards before Monday’s match.

On Wednesday, the 33-year-old Nadal’s 41st career Grand Slam quarterfinal will be against No. 5 Dominic Thiem in a rematch of the last two French Open finals, both won by Nadal.

Nadal vs. Kyrgios was fascinating to watch because of the quality of the play and the subplot of their negative feelings toward each other.

“When I criticized him in the past,” Nadal said, “it’s because I thought he did a couple of things that are not the right image for our sport and for the kids.”

They traded verbal barbs through the media last year after Kyrgios beat Nadal at a tournament in Mexico (which is why a spectator kept yelling “Acapulco!” in the stadium Monday). When they met again at Wimbledon — with, coincidentally, the exact same scoreline as Monday — Kyrgios ripped a shot right at Nadal’s midsection, then refused to apologize.