The defending champion trailed 4-1 in the opening set, but regained command with 20 unanswered points and calmly closed out a 6-4 6-3 win over the Spaniard.
A tricky task against the experienced Verdasco appeared even more testing for Federer when he dropped his opening service game, sending a mishit forehand past the baseline.
But the Madrid man???s success was quickly snuffed out by Federer, who won five straight games to love in an extraordinary run to take the first set.
Verdasco was soon broken again in the second and struggled to put another dent in the Swiss star???s serve, with Federer winning 83 per cent of his first service points.
A sweeping forehand pass sent Federer into the next stage of the tournament, where he will face Richard Gasquet.??
The Frenchman saved one match point during a 6-4 3-6 7-6 win over Spanish seventh seed Roberto Bautista Agut.