The third seed from Bratislava, playing in his first Tour final, raced into a 4-0 lead after breaking Fognini in his first two service games before taking the opening set.
Klizan, 23, looked much fresher than his fourth-seeded opponent despite having beaten top seed Mikhail Youzhny in a semi-final that lasted nearly four hours on Saturday.
Both players suffered from nerves in the second set, surrendering serve for five consecutive games before world number 45 Klizan clinched a well-deserved victory with a deft drop shot after 69 minutes.
