The Italian's 7-5 7-6 (7-4) victory on Tuesday (Wednesday AEDT) extended his record run of consecutive sets won at ATP Masters 1000 events.
Sinner edged a tight opening set before facing an even sterner test in the second, where he trailed 2-5 as Michelsen raised his level from the baseline.
The Italian fought back to force a tiebreak, which he closed out to maintain his perfect record against the American and further stretch his unprecedented run of consecutive sets won at Masters 1000 level to 28.
"I felt like the serve helped me quite a lot today, especially in important moments and in the tiebreak, so I'm happy about that," Sinner said in his on-court interview.
"I know that if I want to go far in this tournament I have to improve from the back of the court. Tomorrow is a day off, which helps me, and I will try to find good rhythm in the practice session. Then we'll see how things go."
Sinner also reached his 20th Masters quarter-final, while keeping alive his bid for a rare "Sunshine Double" after lifting the title at Indian Wells this month without dropping a set.
The 24-year-old could become the first man since Swiss superstar Roger Federer in 2017 to win both US hardcourt Masters events in the same season.
In other results, Sebastian Korda couldn't back up his third-round upset win over world No.1 Carlos Alcaraz.
The American lost his round-of-16 clash with another Spaniard, world No.151 Martin Landaluce, who won a three-set thriller 2-6 7-6 (8-6) 6-4.
Czech No.21 seed Jiri Lehecka also defied the rankings with a 6-4 6-7 (4-7) 6-2 win over sixth-seeded American Taylor Fritz.
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