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Alcaraz and Fritz's Miami quarter-final was postponed to Thursday with persistent rain forcing the evening session in Miami to be cancelled.
The other quarter-finals between 14th seed Karen Khachanov and 25th seed Francisco Cerundolo along with fourth seed Daniil Medvedev and qualifier Christophr Eubanks were also re-scheduled for Friday.
The Sinner-Ruusuvuori clash was also impacted by a two-hour rain delay, but the Italian prevailed to maintain his perfect record in Miami, having not dropped a set.
"We both played well today but I won the important points," Sinner said. "It's never easy when you are up and you get interrupted, but I came back and played well."
Sinner's run to the Miami semi-finals has seen him drop the fewest games (23) since Rafael Nadal (21) and Novak Djokovic (23) in 2014.
The Italian became the seventh male to reach the semi-finals at both Indian Wells and Miami in a single year before turning 22, joining an elite list in Andre Agassi (1990), Jim Courier (1991), Djokovic (2007), Andy Murray (2007 and 2009), Nadal (2008) and Alcaraz (2022).
Sinner's 2023 record is now 20-4, bettered only by Medvedev (26-3) and Cameron Norrie (21-5).