Nishikori had not won at the ATP Masters 1000 level since 2021 at Indian Wells.
"It's been a long time," Nishikori said in his on-court interview.
"It means a lot, especially the way I played in the third set. First and second set, many ups and downs and I was missing a lot of balls. Third set, I was playing pretty good tennis.
"I think, good defence and, when I needed to, I was having good movement and playing aggressive. It was working really well."
A former world number four in 2015 now at 576th, Nishikori needed two hours and 33 minutes to oust the 19-year-old Michelsen, ranked 55.
He fired 29 winners and converted four of 12 break points, to 3 of 4 for Michelsen, who had seven double faults.
"I just needed to keep believing in myself, that's the only thing I can do," said Nishikori, who has 12 tour-level titles.
"To be aggressive, start hitting more forehands and backhands (down the) line. I think that started working well in the second set."
In other main-draw matches, 16th-seeded Karen Khachanov of Russia downed Canadian wildcard Gabriel Diallo in straight sets, 6-4, 6-4, and Argentina's Tomas Martin Etcheverry needed three sets to oust Chile's Nicolas Jarry 7-6, 6-7, 6-2.
Etcheverry was four of eight on break-point opportunities. Jarry was two of four, and his 38 winners and 15 aces were undermined by five double faults and 37 unforced errors.
Portugal's Nuno Borges rallied to beat Serbia's Miomir Kecmanovic 5-7, 6-4, 6-4, while Italy's Lorenzo Sonego won a battle with the Netherlands' Tallon Griekspoor 7-6, 5-7, 6-4.
In Tuesday night action, 13th seed Holger Rune of Denmark outlasted Spanish lucky loser Roberto Bautista Agut for a 6-2, 3-6, 6-2 victory. Rune had to withdraw from the Olympics due to a wrist injury, but he bounced back to improve to 13-2 in first-round matches this season.
"It was a challenge for sure," Rune said.
"It's never easy coming back after a little break - not the longest break, but for me, I'm very young and luckily I haven't been injured much. It was difficult, but I think I managed to find the rhythm quickly."
Rune is off to face another Spaniard, Pablo Carreno Busta, who, while playing on a protected ranking, downed Hungary's Fabian Marozsan 6-7, 7-6, 6-3 on Tuesday.
Number 15 seed Alejandro Tabilo of Chile also prevailed, defeating American Frances Tiafoe 6-4, 6-2.
