Roddick finished off the whitewash by posting a 6-4, 7-6 (7-5) win over Karol Beck. Replacing veteran Pete Sampras, Blake rallied to beat Ladislav Svarc, 4-6, 6-3, 6-0.
The United States registered its 100th Davis Cup victory on home soil.
Roddick improved his singles record in the competition to 5-0, marking the best start to a Davis Cup career by an American since Andre Agassi won seven straight during the 1998 and 1999 tournaments.
Blake has won all three singles and one doubles match in Davis Cup play.
The Americans will face Spain in the quarterfinals. Younes El Aynaoui of Morocco defeated Juan Carlos Ferrero of Spain, 7-6 (7-2), 6-0, 3-6, 0-6, 6-3, to knot the contest at two matches apiece.
But Spain's Alex Corretja was leading Karim Alami, 6-3, 6-0, when the Moroccan was forced to retire due to an injury.
The Czech Republic finished with a 4-1 victory over Brazil. Flavio Saretta collected Brazil's only point with a 6-1, 7-6 (8-6) win over Jan Novak. But Bohdan Ulihrach confirmed the Czech Republic's dominance, routing Andre Sa, 6-1, 6-2.
The Czechs likely will encounter a much sterner test in the quarterfinals against defending champion France.
France secured a win over the Netherlands when Sebastien Grosjean outlasted Sjeng Schalken, 6-2, 1-6, 7-6 (8-6), 2-6, 6-3. Edwin Kempes of Netherlands defeated Arnaud Clement of France, 7-6 (7-5), 6-3, to make the final margin a more respectable 3-2.
Russia also recorded a 3-2 triumph over Switzerland. In the final singles match, Marat Safin posted a 6-1, 7-6 (8-6), 6-3 triumph over Michel Kratochvil. Swiss star Roger Federer had tied it up with a 7-6 (8-6), 6-1, 6-1 win over Yevgeny Kafelnikov.
The Russians will clash with the Swedes in the next round. Trailing after Saturday's doubles loss, Thomas Enqvist rolled to a 6-4, 6-2, 6-4 victory over Tim Henman. Jonas Bjorkman sealed the comeback win with a 4-6, 6-3, 7-5, 6-4 triumph over Greg Rusedski.
The quarterfinals will be played from April 5-7.