Local boy Ferrer, currently number five in the world, broke Verdasco's serve for the first time in the eighth game, before a full house in the emblematic Agora building, and never looked back against the world number 24.
Ferrer shares ownership of the rights to the Valencia tournament with another local hero and ex-world number one, Juan Carlos Ferrero, who was another first-round winner, beating Russian Igor Kunitsyn 6-4, 7-6 (6-2).
"You are always a little more nervous playing in front of your home crowd but I kept improving as the match went on," said Ferrero.
Also in the first round, world number eight Jo-Wilfred Tsonga struggled to a 4-6, 7-5, 6-2 victory against wild-card entry Javier Marti from Spain.
Perhaps tired from his exploits in winning the Vienna Open on Sunday, when he beat Argentinian Juan Martin del Potro in three sets, the Frenchman struggled to get going against the Spaniard ranked 182 in the world.
He soon recovered from that to take a tight second set, however, before comfortably controlling the decisive third.
Tsonga now goes on to meet Sam Querrey of the USA, who beat Latvia's Ernests Gulbis 6-3, 6-4, for a place in the last eight.
Success in Valencia will help Tsonga in his quest to qualify for the ATP World Tour Finals in London later this month.
Two other players who can still qualify for the London event had mixed fortunes in the first round on Tuesday.
Third seed Gael Monfils of France made light work of Spain's Albert Montanes to progress 6-3, 6-1 in exactly one hour and now faces another Spaniard, Pablo Andujar, for a place in the last eight.
Meanwhile, Spain's Nicolas Almagro, currently ranked 11th by the ATP, lost 6-4, 3-6, 6-4 to Argentine Juan Monaco in a titanic late-night struggle; a result that will dent his hopes of attaining a top-eight ranking before the London event.
In other first-round matches, Kevin Anderson of South Africa beat Martin Klizan of Slovakia 6-1, 6-4, while another Spanish victor was Marcel Granollers, who beat Alexandr Dolgopolov of the Ukraine 6-3, 6-4.