The first set went the way of Spaniard Verdasco, who required just one break of serve to open up an advantage.
However, Raonic responded positively in the next set and ensured that a decider was required when he broke Verdasco on two separate occasions.
It ended up being an evenly contested third set, with neither player able to claim what would have been a decisive break of serve. Consequently, a tie-breaker was needed to determine who would advance through to round three.
Raonic appeared to be heading for a straightforward win when he opened up a 4-1 advantage, but after the change of ends, Verdasco managed to haul himself level at five points apiece.
Serves were then traded, before Verdasco finally made a crucial impact to win 9-7.