This is the 7th meeting between the two nations, with Brazil holding a 4-2 lead, and having won the last two match-ups.
Both nations started in Americas Group I this year. Brazil defeated Colombia to reach this stage, while Ecuador overcame Canada and Peru.
Brazil is contesting the World Group Play-offs for the 4th successive year, and is looking to qualify for the World Group for the first time since 2003.
Ecuador has won its last 5 ties, having won Americas Group II last year and is through to this stage for the first time since 2005. Ecuador has only played in the World Group on four previous occasions, most recently in 2001.