Murray started well in a tense first set, but failed to create any break points. The duo continued to hold their serves up until 5-5, when Sinner broke Murray and then held to win the opener 7-5.
The second set proved to be a lot easier for the 20-year-old, who broke Murray early on and carried his momentum to seal a 7-5 6-2 victory.
Sinner has enjoyed a stellar start to his career so far, with the Italian already climbing up to world No.10. But following the match's conclusion, he admitted to feeling some pre-game nerves.
"There were some nerves - I lost my last match against him. I tried to stay focused about my game and it worked.
"Thanks for the support as always. I think I played well, especially in the first set when it was tight in some moments."
Sinner also took a moment to praise his opponent, describing Murray as a "legend".
"It is a special feeling (to share the court with Murray)," Sinner said in his on-court interview.
"He is a legend. Winning three Grand Slams, many, many tournaments and he has had some unfortunate moments with surgeries. His fighting spirit is incredible."
After progressing to the quarter-finals, Sinner resumes his Dubai Open campaign on Wednesday when he takes on the tournament's fifth-seed, Hubert Hurkacz.
As for Murray, the current world No.89's top priority will be finding a new permanent coach. After splitting with long-term mentor Jamie Delgado ahead of the 2022 season, a number of failed trail periods has left the 34-year-old without any trainer.
With the 'Sunshine Double' of Indian Wells and Miami fast approaching, Murray will ideally want to have at least a temporary coach sorted before tackling more tournaments.
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