The former Wimbledon runner-up and recent Madrid Masters finalist destroyed Roddick from the back of the court with a barrage of powerful groundstrokes.
Later, Radek Stepanek clinched the win for the Czechs with a comprehensive 6-2 6-1 thrashing of fading American star James Blake.
It was a second successive victory for the Czechs in the Red Group and they now have an insurmountable 2-0 lead in the best-of-three matchup, which will conclude with a doubles rubber on Wednesday.
The USA were beaten comfortably by 2011 World Team runners-up Argentina in their opening affair.
In the blue group, Serbia improved to 2-0 with a victory over Russia on day two.
Four-time World Team winners Argentina also assumed a 1-0 lead against Japan as Leonardo Mayer outfought Tatsuma Ito 6-4 6-4.
Germany won a record-breaking fifth title with victory over the 2010 champions Argentina last year on the red clay at Rochusclub.