The 31-year-old managed to see through a 4-6 6-3 6-2 victory over his fellow countryman to progress to the next round.
The contest was fairly well matched with both players forcing the break of serve in the second and third match of the first set.
Despite an even start to the game, Verdasco managed to edge the first set while his fellow Spaniard drew the match level after claiming the second set by three games.
The third set was another close encounter with the majority of games being won on the serve, but Ferrero's form led him to victory over the 27-year-old.
The Spaniard will face either Milos Raonic or David Ferrer in the third round of the competition.