Olympic Gamed gold medallist and third seed Zverev fell behind a break in both sets but battled past Murray in straight sets at the ATP Masters 1000 tournament on Wednesday (AEDT).
Tsitsipas – the second seed – rallied from a set down to vanquish Fabio Fognini in the desert, while fifth seed Berrettini was a third-round casualty.
Having already defeated Novak Djokovic, Rafael Nadal and Roger Federer in his career, all that was missing for Zverev was a win over Murray to complete the 'Big Four' sweep.
Zverev added Murray to his list of scalps with a 6-4 7-6 (7-4) victory to reach the Indian Wells fourth round for the first time since 2016.
The German star has now won 19 of his last 20 matches since Wimbledon.
"He's the only one of the Big Four that I hadn't beaten yet, so I'm happy that I've done it today," said Zverev, who will clash with 14th seed Gael Monfils in the next round. "Obviously it was a fantastic match.
"I thought Andy played extremely well, maybe as well as he's played since the surgery. I hope he continues playing the same way, because tennis did miss him for a long time and I think it's good to have him back."
It was far from easy for Greek star Stefanos Tsitsipas, who prevailed 2-6 6-3 6-4 against 25th seed Fabio Fognini.
Tsitsipas added to his ATP Tour-leading haul of match wins this season, which now stands at 53 after Fognini had been looking to score his first victory over the French Open runner-up.
Alex de Minaur – the 22nd seed – awaits after he took down 13th seed Cristian Garin 6-4 6-2 for his first trip to the Indian Wells last 16.
Wimbledon finalist Berrettini was no match for Taylor Fritz, who surprisingly topped the Italian 6-4 6-3.
Berrettini entered the contest as the only player on the ATP Tour this season to register double-digit wins on three surfaces – 15-4 (hard), 13-4 (clay) and 11-1 (grass).
"We're coming to the end of the year, I could really use a big result," said Fritz after claiming his first top-10 win of the year. "This is just what I needed, playing one of my favourite tournaments close to home."