Fourth seed Dimitrov was pushed to five sets by American Jared Donaldson in the previous round and once he failed to convert four set points in the 12th game of the opener against Verdasco and lost the ensuing tiebreak, he looked flat.
The aggressive left-handed Spaniard broke twice in the second set and although he allowed Dimitrov back from 4-2 in the third, he broke again to claim his third career win against the 27-year-old.
Verdasco has now reached the last 16 in Paris for the seventh time and will hope to finally break through that barrier having fallen at that stage on six occasions.
