The left-handed Spaniard won 10 of the first 11 games to lead by a set and 4-0. But Verdasco, who dropped out of the top 10 to No. 15 this year, let Gil back into the match by losing five games in a row.
Verdasco committed seven double-faults and Gil focused on the less reliable backhand. Gil, who became the first Portuguese to make an ATP final here last year, forced Verdasco to a tiebreaker but couldn't win it.
Raonic, who in February became the first Canadian to clinch an ATP Tour title since 1995, has improved 130 spots in the rankings this year to No. 27.
The top three seeds in the women's competition exited in the quarterfinals.
Top-seeded Alisa Kleybanova lost 6-4, 6-2 to Kristina Barrois, and Monica Niculescu rallied to overcome second-seeded Jarmila Gajdosova 5-7, 6-4, 6-2. Anabel Medina Garrigues upset third-seeded Klara Zakopalova 6-3, 7-5.