The tournament is the last chance for some players to gain one of the last three remaining spots for the ATP World Tour Finals in London.
Cilic hit a forehand winner to take the first set but Verdasco bounced back by jumping to 3-0 leads in the second and third sets.
"It's slower than last year," Verdasco said. "I prefer maybe a little bit more this court because it's slower and I have more time to prepare my shots."
Verdasco is hoping to be on the Spain team for the Davis Cup final next month.
"If I play Davis Cup, then I will try to prepare and get ready for that final the best as possible," Verdasco said. "And if I'm not, at least finish well here."
Benneteau defeated Milos Raonic of Canada, 6-7 (5), 7-6 (5), 6-4, setting up a match with 13th-seeded Andy Roddick. The French wild card reached the final of the Winston-Salem Open in August and has improved his ranking to No. 54 after being No. 87 six months ago.
Garcia-Lopez edged Colombian qualifier Santiago Giraldo 6-4, 1-6, 6-4 and will next play sixth-seeded Jo-Wilfried Tsonga of France. Giraldo slammed his racket to the ground after netting backhander to lose the match.
Anderson had 13 aces to outlast Gilles Muller of Luxembourg 6-3, 4-6, 6-4.