Achieving a hold to love in the opening game, 30-year-old Norrie’s strong start faded quickly as Sinner broke twice to dominate the first set 6-2.
Each held serve until the fifth game when Norrie, having resisted a break point, attempted to seize momentum with an underarm serve but it failed to clear the net.
The Italian claimed the game, but Norrie broke back, winning seven successive points in his efforts to turn the tide in a first competitive meeting between the players.
At 5-5, the British number one survived two break points before surrendering the game to Sinner, who served out in the final game to become only the second player in tennis history to win the first 20 Masters 1000 matches of the season, after Novak Djokovic in 2011 and 2015.
“We know each other quite well. We practised a lot in the last tournament. We both kind of knew what to expect,” the four-time Grand Slam champion said of Norrie.
Speaking to Sky Sports, he added: “This surface is very very different to all the other surfaces so it’s very tough to get the right feedback and sometimes you feel like you are not playing your best.
“But I’m very happy to be in the quarters again, it’s a tournament I haven’t played a lot so it means a lot to me and I’m happy to be through in two sets.”
In the quarter-final he will play either Kopriva or Jodar, who meet later on Tuesday. The pair were given the afternoon slot after Jodar’s round of 32 win over Joao Fonseca finished late on Sunday night.
After playing at the “unusual” time of 11am local time (12:00 BST), Sinner questioned the way that the tournament is organised.
“[Jodar] finished very, very late [on Sunday], but at the same time I feel like we need to make some adjustments with scheduling of the day,” he said.
“For matches at 8pm, it’s very very late, even though you have one day in between – still, it’s very very late.
“You finish at 1.30am and you need to eat, you need to have treatment, so it’s very late. We try to adapt ourselves, our bodies and minds.”