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 play for Spain in next month's Davis Cup final.
"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."
Verdasco's next opponent is fifth-seeded Tomas Berdych of the Czech Republic.
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.
Kohlschreiber defeated Mikhail Youzhny of Russia 6-4, 6-2. The German qualifier broke to lead 4-3 in the opening set before going 4-0 up in the second.
Garcia-Lopez edged Colombian qualifier Santiago Giraldo 6-4, 1-6, 6-4 and next plays sixth-seeded Jo-Wilfried Tsonga of France. Giraldo slammed his racket to the ground after netting a backhand to lose the match.
Anderson had 13 aces to outlast Gilles Muller of Luxembourg 6-3, 4-6, 6-4.
Mahut was playing for the first time since withdrawing from a second-round match at the Valencia Open following the death of his 2-year-old nephew eight days ago.