Sweden's Peterson, a recent winner in Nanchang, recovered from a dreadful first set to defeat Ons Jabeur 0-6 6-4 7-5 in the first semi-final on Sunday (AEDT).
She will meet Watson in the final of the WTA International event after the Briton won in straight sets against Veronika Kudermetova, triumphing 6-1 6-4 in 74 minutes.
Peterson suffered a bagel in the opener of her match, although the set was closer than the scoreline suggested as the first five games went to deuce.
In the second set, Peterson missed a chance to serve it out at 5-3 but then broke Jabeur in the next game to level the contest.
She fell 3-1 behind in the decider before winning six of the last eight games to progress from a hard-fought encounter in two hours and six minutes.
"It was a really tough match," Peterson said. "[Jabeur] played well, I couldn't find my rhythm and I had to fight for every point so I'm happy that I got the win in the end."
Watson made her first WTA final in three-and-a-half years, winning the first set with ease as Kudermetova, ranked 80 places above her, did not earn a single a break point.
One break was enough to settle a closer second set, with world No.125 Watson converting her third match point.
She has won all of her previous three finals on the main tour, while Peterson's Jiangxi Open success in September was her only prior such contest.