The 2014 US Open runner-up, prevailed 7-6 (7-5) 7-6 (7-5) after a tough battle against the No.63-ranked 29-year-old Sydneysider in the Atlanta Open.
Nishikori had not played on tour since Indian Wells in October 2021. He then underwent hip surgery in January 2022 and was out of action for more than 17 months.
He returned to competition in June, winning a Challenger Tour event in Puerto Rico.
"I'm really happy the way I played today," Nishikori said.
"I played a couple of Challengers in the last couple of weeks, but today against Jordan it's a different level than playing in the Challengers.
"First game I was like, 'Oh, I have to play good today', and I did. I did quite well today."
Nishikori, 33, has fallen to No.439 in the ATP Tour rankings.
He reached No.4 in 2015, shortly after his semi-final victory over Novak Djokovic at the US Open made him the first male grand slam singles finalist from Asia.
In other round of 32 action in Atlanta, Aleksandar Vukic progressed 7-6 (7-5) 6-3 against the USA's Ethan Quinn, while Thanasi Kokkinakis recovered from a nightmare first set to beat French veteran Gael Monfils 1-6 6-3 7-6 (7-5).
James Duckworth won his first set against South Africa's former world No.31 Lloyd Harris before falling 6-3 3-6 2-6, and Max Purcell lost in straight sets to Brandon Nakashima, of the US, 3-6 6-7 (5-7).
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