France's Gasquet gained the final with a 6-4, 7-5 victory over Croatia's Ivo Karlovic. The world No. 10 will be seeking his 10th career title and third of the year after also winning at Doha and Montpellier.
Gasquet is vying for one of the remaining four berths in the season-ending ATP World Tour Finals.
His Moscow opponent will be the surprising Kukushkin, who upended second-seeded defending champion Andreas Seppi of Italy 6-1, 1-6, 6-4 in the day's first semifinal.
The 102nd-ranked Kukushkin reached just his second career ATP final with the result.
Seppi, meanwhile, fell to 0-5 in semifinals this year.