Murray 'deserved to win' after opening victory against Berrettini
The unseeded Murray battled with Italy's Berrettini for nearly five hours at Rod Laver Arena and even saved a match point in the final set before prevailing 6-3 6-3 4-6 6-7(7) 7-6(10-6).
The 35-year-old Briton had been knocked out in similar marathon matches at Grand Slams in recent years and said he took pride in shutting down those who questioned whether he could still perform at the biggest events after hip surgeries.
"I felt very proud of myself after the match. That's not something that I generally felt over the years at the end of the tennis matches. I was impressed with myself, which again is not something... I'm hard on myself usually," Murray said.
"Yeah, tonight I need to give myself some credit because the last few years have been tough. I've lost a few of those type of matches in the Slams the last couple years.
"Whether that's the (Stefanos) Tsitsipas match (at the US Open) or (John) Isner at Wimbledon, that one could have gone the other way tonight, but I stayed strong and I deserved to win."
Murray credited his form to the work he had put in during the off-season in Florida and reuniting with coach Ivan Lendl, who had helped him win three Grand Slam titles.
"Obviously the past success that we've had gives me confidence in the relationship," Murray said.
"Most of my biggest wins have come whilst Ivan was part of the team. He's certainly not going to let me get away with not working hard. He's always going to push me as hard as he can to try and get the best out of me."
Dan Evans was also impressed with Murray's victory and was amazed that his fellow Briton did not cramp up.
"He obviously had troubles with the cramping and I think he will be happy that he did his pre-season and he got everything right," Evans said.
"He spoke a bit about the nutrition and then the work, so he obviously addressed that.
"He's pretty negative, and when he says he was playing well... Obviously he feels he's hitting the ball well if he gives himself a compliment."