Verdasco took control in the opening game of the match, breaking his French opponent before holding to move into a 2-0 lead.
The set remained on serve from that point, with Verdasco moving into a one-set lead.
It was a similar story in the second with Verdasco securing the only break at 1-1 before taking control of the set.
De Schepper had two chances to break back in the latter stages, but the Spaniard held on to move two sets ahead.
De Schepper responded in the third as the Frenchman secured an early break to go 4-1 ahead, but back-to-back breaks for Verdasco handed the Spaniard the chance to serve for a spot in the next round.