The 25-year-old is ranked 102nd in the world but produced a fine display to advance past Italy's Seppi as he continues his search for a first ATP Tour title in almost three years.
The Russian-born player stormed ahead by taking the opening set 6-1 but was given a warning of Seppi's ability when the world ranked number 22 struck back and took the second set by the same margin.
But Kukushkin hung on and won the decisive third set 6-4 to set up a final against top seed Richard Gasquet on Sunday.
Gasquet had little trouble reaching the final as he won his own semi-final in straight sets, easing past Croatian Ivo Karlovic 6-4 7-5. Karlovic's 15 aces brought no reward.
The women's final will be contested between Simona Halep and Sam Stosur after both advanced with straight-sets victories over Russian players in their respective semi-finals.
Romanian fifth seed Halep needed just one hour 15 minutes to beat Anastasia Pavlyuchenkova 6-2 6-1.
Australian Stosur was also comfortable as the seventh seed achieved a 6-2 6-4 win over Svetlana Kuznetsova.