Federer, the world No. 1, defeated Spaniard Nicolas Almagro, 6-3, 6-4.
Federer was last year's Rome runner-up to Spaniard Rafael Nadal, who is seeded second at this tournament and is the two-time defending champ.
Blake beat Frenchman Gael Monfils, 7-6 (7-4), 6-3.
Three other seeds reached the second round, as No. 12 Czech Tomas Berdych beat Finn Jarkko Nieminen, 6-4, 7-5; No. 13 Frenchman Richard Gasquet beat Spaniard Fernando Verdasco, 6-1, 7-5; and No. 15 Russian Mikhail Youzhny beat Frenchman Julien Benneteau, 6-1, 3-6, 6-2.
2014 amfAR Inspiration Gala [PHOTOS]
Julius Randle breaks leg during NBA debut