Mayer put the Argentines up 1-0 on Day 1 in Dusseldorf with a 6-4, 5-7, 6-3 win over Harrison, and Berlocq followed that up with a 6-2, 6-2 spanking of Roddick, needing just 90 minutes.
Also in the Red Group at the event are the Czech Republic and Japan.
Only one match was completed between them Sunday, with Japan's Tatsuma scoring a 3-6, 6-4, 6-4 win over Radek Stepanek.
In Blue Group play, defending champion Germany opened a 1-0 lead over Russia and Serbia established a 1-0 edge over Croatia.
2014: The Year in Music [PHOTOS]