Verdasco, the top seed and 2008 champion, converted five of 18 break points in the second-round victory.
Gulbis served eight aces but could not overcome Verdasco, who picked up his game in the third set.
"It was a difficult match," Verdasco said, describing Gulbis as "a player that hits the ball very hard and it is difficult to play against him."
"Hopefully, it will be another good week like in 2008."
Dolgopolov, who last year won his first ATP title here, didn't drop serve.
Fifth-seeded Carlos Berlocq beat fellow Argentine Marco Trungelliti 7-6 (4), 4-6, 6-1. Berlocq converted eight of 16 break points, but his five double faults helped to keep Trungelliti in it.