"These courts helped me a little bit," Paul said. "They're not jumping quite as high as some of the other courts we've played on. Kept the ball in my strike zone a little bit more.
"Didn't serve as well as I would have liked to but somehow squeaked out a lot of those service games so that was huge."
Paul snapped a six-match losing streak against top-20 opponents to reach his fourth career ATP final.
"If I get broken I feel like the set is over so it's high pressure the whole match with him," Paul said.
Paul, who won his only ATP title at Stockholm in 2021, lost his only other tour finals last year at Acapulco and Eastbourne after a run to his first Grand Slam semi-final in the 2023 Australian Open.
In his first ATP semi-final since last year at Toronto, Paul dispatched the 21-year-old left-hander to level his record against Shelton at 2-2.
Paul beat Shelton in last year's Australian Open quarter-finals but lost to him in the fourth round at last year's US Open as well as in Tokyo, where Shelton took his first ATP title last October.
Paul broke for a 3-2 lead and reeled off four games in succession to capture the opening set.
In the second set, Shelton sent a backhand volley wide to surrender a break and give Paul a 2-1 edge. They both held serve from there until the end.
World number 67 Giron, who lost his only ATP final in 2022 at San Diego, upset US top seed Frances Tiafoe in the quarter-finals.
World number 17 Mannarino, a winner in his past three ATP finals, seeks his sixth tour title after lifting trophies at Rosmalen in 2019, Winston-Salem in 2022 and last year at Newport, Astana and Sofia.