Troicki, the No. 6 seed, defeated Joao Souza 6-4, 6-2 while losing just six points in nine games serving. He took 36-of-42 (85 percent) of the points on serve.
Souza won more than 60 percent of the points when serving but Troicki finished off three of his eight break chances to move to the second round.
Verdasco, seeded eight and coming off a quarterfinal appearance at Wimbledon, stopped Andreas Vinciguerra 6-5, 7-6 (7-3). He had 12 aces and lost 11 points -- five on double faults -- when serving.
Henri Laaksonen claimed a 5-7, 6-1, 6-1 decision over Antonio Veic in a battle of qualifiers. It was the only match Tuesday to go three sets.
Filippo Volandri pasted Jurgen Zopp 6-1, 6-2 in 53 minutes. He took nearly three-quarters of the points when Zopp served.
Also Tuesday, Albert Ramos beat Julian Reister 6-3, 6-3; Blaz Kavcic advanced over Marius Copil 6-4, 6-1; Jan-Lennard Struff ousted Sergiy Stakhovsky 6-3, 6-3; and Guillermo Garcia-Lopez was a 7-6 (7-4), 6-1 winner over Jan Hajek.