The Russian, who won his only previous final appearance at the 2016 Chengdu Open, was in superb form to record a 6-3 6-2 success.
Khachanov, ranked 30 places lower than his opponent, seized upon four of the 14 break-point openings he created to get the job done in just under 75 minutes.
He will now take on Pouille after the Frenchman ended the remarkable run of world number 193 Ilya Ivashka.
Qualifier Ivashka, who was the beneficiary of Stan Wawrinka’s injury-enforced withdrawal earlier in the tournament, suffered a 6-3 7-6 (8-6) reverse.
Pouille, seeded third, has already won this year in Montpellier, having claimed three titles in 2017, during which he climbed to a career-high 13th in the rankings.
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