The seventh-seeded Croatian started slowly, dropping the first set 1-6, but then turned it on, finishing in 6-0, 6-3 fashion to move past Slovakia's Klizan.
This year's Valencia field is topped by Spain's David Ferrer and will also feature the retirement of former world No. 1 and Spanish favorite Juan Carlos Ferrero.
Ferrer said he considers Ferrero a colleague and friend, calling him "one of the best Spanish players in history."
The world's fifth-ranked player said the Valencia Open was coming during a 2012 season he called "my best year," while admitting that playing "at home ... for your people" has put some extra pressure on him.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys