On the bright lights of Rod Laver Arena, she turned it on against the American qualifier, winning 6-1, 6-1 in 63 minutes.
In recent years, the mercurial Kyrgios has often let code violations hamper the outcome of a match.
"@RodLaverArena is one of the greatest atmospheres on the tour without a doubt". Obviously feeling pretty good after Brisbane. I felt a lot of pressure every time I went out on the court. "I would like to be a bit of a better role model with some of my behavior, but I guess that will come in time".
Kyrgios' openly admitted in the past to having problems to stay determined - but a strong start to the year suggests that the Australian is eager to deliver this year.
"It's a positive start with a good result". If I lose a match, at the end of the day it's a tennis match.
"I can't expend too much energy on other things. I've played a lot of them now".
Rafael Nadal sailed into the second round of the Australian Open on Monday with a comforatable 6-1 6-1 6-1 win over Dominican journeyman Victor Estrella Burgos.
Roger Federer rates Kyrgios a threat to the established order in the year's opening Grand Slam, but says the volatile Australian is a work in progress.
These two have played once, which was in last years Canadian Masters, a match Kyrgios won in straight sets.
"I just hope he concentrates a little more on his tennis because it would be wonderful for the sport".
"I'm not putting expectations on myself and no-one in my team does", she said.
"Toni is the most important person in my career", he added.
Murphy reacted, saying: "Because I'm not going to do it after one guy (yells out)".
Kyrgios, who made the Australian Open quarterfinals in 2015, will begin his 2018 campaign against Brazil's Rogerio Dutra Silva.
"I feel like we've got more depth than ever", she said.
But Kyrgios swept through the second set in just 23 minutes and again broke the Brazilian in the seventh game of the final set to close out the match.
Nick Kyrgios won his first Aussie title at the Brisbane International. Today, he was two sets to love down and obviously it didn't faze him very much. "He's a tough competitor".
He was accused of "tanking" a match against Richard Gasquet at Wimbledon in 2015 and was booed by his own fans past year when he suffered a meltdown to lose to Andreas Seppi in five sets in the second round at Melbourne. Some have suggested the fact that Kyrgios' girlfriend, Ajla Tomjlanovic, is back on the WTA Tour after an injury hiatus has helped his newfound attitude. "I know what he's going to bring". "Got to keep things rolling".