In a close first set, the world number two squeezed past his opponent in the tie break 7-5.
Verdasco, who matched Nadal throughout, pulled the contest level in the second with a 7-4 win in another tie break.
The third set went to a tie break again and Nadal overpowered his fellow Spaniard before relinquishing three match points to give Verdasco a chance. However, Nadal eventually finished the tie off, winning 11-9.
His next match will be against Mardy Fish, who defeated Richard Gasquet in straight sets.