The world number 12 had to recover from a set down to beat the Russian in two hours and 28 minutes in what was a gruelling semi-final to seal his progression through to the tournament showpiece.
Cilic will next take on fourth seed Jurgen Melzer of Austria, after the world number 29 beat Robin Haase 7-6(2) 6-3 on the indoor surface.
ATP Zagreb results
1-Marin Cilic (Croatia) beat 3-Mikhail Youzhny (Russia) 4-6 6-4 6-3
4-Jurgen Melzer (Austria) beat Robin Haase (Netherlands) 7-6(2) 6-3
ATP Montpellier results
3-Richard Gasquet (France) beat Jarkko Nieminen (Finland) 6-3 3-6 6-2
8-Benoit Paire (France) beat Michael Llodra (France) 4-6 6-3 6-1