As the set wore on she suffered cramping in her leg and was nearly unable to run, allowing Kasatkina to produce the deciding break in the 10th game to wrap up the victory.
"It was very tough and I saw you gave everything today and that's what sport is all about", Kasatkina told Jabeur at the trophy presentation.
"This is really wonderful and I'm really happy".
In Saturday's final, Jabeur will face sixth-seeded Daria Kasatkina of Russian Federation, last year's runner-up, who put out Britain's Johanna Konta 6-4, 6-3.
"She (Jabeur) plays interesting tennis with plenty of drop shots, often advances to the net", Kasatkina said.
The world number 14 took her first and only WTA singles title at the 2017 Volvo Car Open in Charleston in the United States when she defeated Latvia's Jeļena Ostapenko for the title. "It was a little bit frustrating because I missed some easy balls, but I said I was just going to play my game, and if it goes, it goes".
Russian competitors have won the women's Kremlin Cup four times in the last five years, with Germany's Julia Goerges beating Kasatkina in last year's final.
Jabeur, the first Tunisian to play in a WTA final, said she meant to be back. "They helped me through the end because it was a little bit hard". "I was crying because I was cramping", tweeted Jabeur.
Jabeur's run to the final included upsets of Ekaterina Makarova, former US Open champion Sloane Stephens, Anett Kontaveit, and Anastasija Sevastova.
Mannarino was 5-3 down in the second set before winning four straight games to close out the match.
The Briton saved a match point at 5-2 but Kasatkina held serve in the next game to reach the Moscow final for the second successive year.
The third-seeded Khachanov won an all-Russian semifinal over Daniil Medvedev 6-1, 6-7 (5), 6-3 to reach his third career final.
Seppi will next face Frenchman Adrian Mannarino, who beat Belarusian qualifier Egor Gerasimov 7-6 (3), 6-3.