The 36-year-old Federer had taken a set from Federico Delbonis 6-3 with the second tied at 2-2 when rain stopped play. After another 90-minute delay organizers suspended play for the night.
But that was about as competitive as things got in the third-round match at the Indian Wells Tennis Garden on Monday.
Elsewhere, US Open victor Sloane Stephens cruised past wild card Victoria Azarenka in straight sets 6-1, 7-5 in a second-round match that was postponed from Saturday night because of rain.
Federer is seeking to extend his ideal record this season to 13-0 as he hopes to make history and capture his sixth title.
Federer has already won two titles in 2018, claiming his 20th Grand Slam crown by winning the Australian Open in January.
With rivals Rafa Nadal, Stan Wawrinka and Andy Murray electing not to enter the tournament, and Novak Djokovic and Kei Nishikori both eliminated, the path appears clear for the Swiss to win a record sixth Indian Wells title.
Verdasco, 34, is making his 15th straight appearance in Indian Wells and trying to improve on his 2009 quarter-final run. I am on a good run right now and I want to maintain that. I am super happy to win and come through this tough opponent and this tough round.
In other action, Croatian Borna Coric defeated 13th seed Roberto Bautista Agut 6-1, 6-3.
Next up for Federer is a meeting tomorrow with France's Jeremy Chardy, who upset his countryman Adrian Mannarino earlier yesterday.
Garcia is trying to improve on her best result here which is reaching the round of 16 in 2015 and past year.