With the crowd largely in the palm of his hand, the Scot raced out of the blocks to take the first two sets under the roof of a muggy Rod Laver Arena.
A five-time runner-up in the tournament, little has come easy for Murray at Melbourne Park, and so it proved again as Berrettini emerged from a long off-court break between sets dialled-in to level the match.
Murray's determination never wavered, though, and he held his nerve in the deciding 10-point tiebreak, closing out the match with incredible fortune as his bunted forehand return caught the net and left Berrettini no chance.
It was a huge win for the 35-year-old Briton, now ranked 66, to knock out last year's semi-finalist for a landmark 50th match-win at the season-opening Grand Slam.
"I'll be feeling this this evening and tomorrow, but right now I'm unbelievably happy and proud of myself," said Murray.
"I've put a lot of work into the last few months with my team to give me this opportunity to perform on stadiums like this, in matches like this and against players like Matteo and it paid off tonight."
Murray will play the winner of Australia's Thanasi Kokkinakis and Italian veteran Fabio Fognini for a place in the third round.
Also in the men's draw, Russia's fifth seed Andrey Rublev ended the tournament of 2020 finalist Dominic Thiem 6-3, 6-4, 6-2 in 36 degrees Celsius (96.8 Fahrenheit) temperatures.
Former US Open champion Thiem was outplayed as he continued his return from a wrist injury which kept him off court for nine months across the 2021 and 2022 seasons.
As the mercury rose, the heat forced play to be halted on outside courts. The roofs were closed on the three main stadiums - Rod Laver Arena, Margaret Court Arena and John Cain Arena.
Play resumed on the outside courts about three hours later.
Britain's Dan Evans, Pablo Carreno Busta of Spain, Bulgaria's Grigor Dimitrov and Diego Schwartzman of Argentina all rolled into round two.
Eighth-seeded Taylor Fritz of the United States defeated Nikoloz Basilashvili from Georgia 6-4, 6-2, 4-6, 7-5.
