Murray has had plenty of joy in Miami since making his debut 18 years ago, winning in 2009 and 2013, and is dreaming of one more shot at glory on his swansong appearance.
He was facing the possibility of a first-round exit as he lost the opening set but he fought back and when Berrettini, playing his first ATP Tour match since the US Open, suffered dizzy spells he pounced to seal a 4-6 6-3 6-4 success.
The Italian is coming back from lengthy injury problems, which showed later in the match, but he started well by breaking Murray in the opening game, sealing it with a blistering forehand down the line.
Murray, 36, missed two chances to break back at 3-2 and that proved crucial as Berrettini's monster serve allowed him to see out the first set.
The second set saw an improvement and Murray's chance came in a marathon sixth game as he broke on the third attempt with a sweet forehand return.
Berrettini's health took a turn for the worse when he was about to serve at 2-5 as he suffered a dizzy spell and needed to use his racket as a crutch to stop him collapsing.
Doctors checked his blood pressure and after a long break, the Italian was able to continue, but Murray soon sent it to a decider.
When the Scot won another 12-minute game on Berrettini's serve in the opening game, the writing was on the wall.
Murray played some clever tennis, running his weary opponent side to side as the former Wimbledon finalist continued to suffer.
He did have to fight back from 0-40 down midway through the decider and that ended Berrettini's challenge as Murray won for just the fourth time in 2024.
Meanwhile, Jack Draper put in an assured performance to beat Taro Daniel and reach the second round.
The Briton, ranked number 42 in the world, overcame his Japanese opponent 6-3 6-2 in 69 minutes to set up a second-round meeting with 22nd seed Nicolas Jarry.
Looking to bounce back from a disappointing first-round exit in Indian Wells, Draper was by far the superior player against the world number 78 in Florida, hitting 25 winners and had a 97 per cent success rate on his first serve.
A run of nine points out of 10 midway through the first set allowed him to assume control, sealing a decisive break with a searing crosscourt backhand.
He served out the set with a flurry of aces and he was soon knocking on the door in the second, missing break points in the opening game.
Draper made his move at 1-1 with a backhand pass which Daniel left and then saw land on the line.
A second break put him on the verge of victory and he saw it out with an impressive hold, taking match point with a crunching forehand.
