World number 14 Fritz beat fellow American Paul 6-3, 7-5 to reach his fifth showpiece match of the season, while 26th-ranked Musetti beat Italian first seed Cobolli 4-6, 6-2, 7-5.
"I thought it was a super high level," ex-world No.4 Fritz said of his clash with 15th-ranked Paul.
"I played so many points as good as I could play and he still beat me. And I think the other way around, too. There weren't many free points on either side. We made each other work for it a lot."
Victory leapfrogged Fritz above Paul into 12th spot in the race to the ATP Finals next month.
Despite a difficult season for former world number five Musetti, his battling win against Roland Garros finalist Cobolli took him into a second final of the year.