Tiafoe gave himself three match points with a backspinning drop volley that landed so close to the net, it bounced back over to his side. Michelsen had already given up pursuit when the ball bounced.
The 26-year-old Tiafoe closed out his first match of the tournament on his first match point when Michelsen put a forehand into the net for Tiafoe’s fifth service break.
The other round-of-16 winners were No. 7 seed Jordan Thompson of Australia, 6-1, 6-1 over American Denis Kudla, and eighth-seeded German Dominik Koepfer, 6-4, 7-6 (5) over Rinky Hijikata of Australia.
Michelsen, who has risen into the top 100 over the past year, had the first break for a 3-2 lead in the first set but immediately gave it back on Tiafoe’s second break point in the next game with one of his four double faults.
After getting another break for a 5-4 lead, Tiafoe lost the first two points while serving for the first set. He won the next four, getting his first set point with a cross-court winner on an attempted drop shot from Michelsen, who then put a backhand into the net.
After a long exchange of sliced backhands and forehands in the second set, Michelsen brought Tiafoe in with another drop shot before watching a lob go over his head.
Tiafoe won 71% of the points when he came to the net to 35% for Michelsen.
“Once he broke me, I really had to up my level,” Tiafoe said. “I wanted to kind of be the aggressor. From there, I played really well, I thought. A lot of creativity, and I got a little lucky at times.”
The 14th-ranked Tiafoe, who lost in the second round of the Australian Open after reaching the U.S. Open quarterfinals last summer, will play American Marcos Giron in the quarters.