If Nishikori goes on to win his first title since 2016 then he will improve to within 125 points of the eighth and final berth in the ATP's Race to London, with next week's Paris Masters to come. He has lost eight straight finals since.
Kukushkin battled hard in the Austrian capital, but was broken when serving to stay in the first set and Nishikori maintained the momentum by breaking again at the start of the second.
Now in ninth place in the race for the ATP Finals, a win would move Nishikori closer to a starting berth for the eight-man event in London next month.
It was a rather slow start for the Japanese, fending off a break point in game two with a smash victor before Anderson found the way to convert the fifth break point in game four for a 3-1 lead when Kei sent a backhand long after a 14-minute thriller.
Cape Town - Kevin Anderson has become the first South African player in 23 years to reach the year-end ATP Finals.
A tense second set required a tie-break to split the two finalists, with Anderson finding his best level on his serve and forehand side.
In Switzerland, Federer moved a step closer to a ninth title albeit he was out of sorts in his 7-6 (7-1) 4-6 6-4 beating of Gilles Simon. He then dropped his serve to love, and let another match point slip in Medvedev's next service game by netting a backhand.
Copil upset expectations of a Federer final against Alexander Zverev in a 6-3, 6-7 (6-8), 6-4 win over the fifth-ranked German in the earlier semifinal.
The towering 32-year-old is also guaranteed to finish the year in the top 10 for the first time, reward for claiming the fifth singles title of his career.
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