Thirty-two years after his father Petr - the 1988 Australian Open champion - won the then-Sovran Bank Classic, the fourth-seeded Korda beat 10th-seeded Flavio Cobolli of Italy 4-6 6-2 6-0 in the final in Washington DC on Sunday.
They are the first father-son tandem to win the same ATP Tour event.
The 24-year-old Korda is the younger brother of golf stars Nelly and Jessica Korda. His mother, Regina Rajchrtova, played on the WTA Tour.
Korda became the first American to win the Washington event since Andy Roddick in 2007. His previous victory came in in May 2021 in the Emilia-Romagna Open, an ATP 250 tournament.
In the women's final, Paula Badosa of Spain won her first title following a back injury, beating Marie Bouzkova of the Czech Republic 6-1 4-6 6-4 in a rain-interrupted final.
The 26-year-old Badosa, ranked as high as No.2 in the world, was sidelined six months last year because of a stress fracture.
"One year ago I was on the couch, so it's a big difference now," Badosa said. "Now I'm an athlete again."
She now has four WTA Tour victories, also winning in 2021 at Belgrade and Indian Wells and in January 2002 in Sydney.
"I was really, really nervous because I really wanted it really bad," Badosa said.
Bouzkova was playing her first WTA 500 final. She won her lone career title in 2002 in Prague.
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