Koepka, 34, shot a seven-under-par 63 in his final round to tie level with Rahm, who shot 65, on 19-under at the Old White course in West Virginia.
In the play-off on the 18th, Rahm’s tee shot left him in a bunker at the back edge and his second shot got him to within 20 ft of the hole.
Koepka made par with ease, piling the pressure on Rahm to match his opponent to stay in the contest.
The Spaniard went agonisingly close but missed his putt for par to hand victory to Koepka.
The win marked Koepka’s fifth LIV Golf title of his career, following wins in Jeddah in 2022 and 2023, Orlando in 2023 and Singapore earlier this year.
“This is probably my favourite one,” Koepka said.
“It’s always good when you have to battle good players.”
Rahm beat Koepka to the 2023 Masters to win his second major and the American said it was nice to get revenge on the 29-year-old.
“Jon is a hell of a player. For whatever reason, he has always gotten the better of me a little bit as of late. It feels nice just to get one.”
Smash, captained by Koepka, won the team title by three shots.