
Wawrinka, the 39-year-old three-time Grand Slam champion who has now slipped to 217th in the world, had beaten Andrey Rublev in the quarterfinals on Friday, his first win against a top-10 opponent for over a year.
But he found the going tough against 27-year-old American Paul, the world No 13.
With Paul 4-2 ahead in the first set, Wawrinka had two chances to break but spurned both.
The American, who won the Stockholm title in 2021, roared through the second set to move into a final against either Bulgarian world No 10 Grigor Dimitrov or Dutchman Tallon Griekspoor, who face off in the other semifinal later on Saturday.