Melzer edged past Igor Kunitsyn 6-2, 6-7 (3-7), 6-4, 3-6, 6-1 behind 84 winners. Haider-Maurer didn't face a break point until the third set of a 6-1, 6-4, 6-7 (1-7), 6-2 win over Alex Bogomolov Jr.
Haider-Maurer had at least one break in each set. He had 17 aces and won 21-of-23 points when approaching the net. Bogomolov had just 15 winners in the match.
Melzer pounded out 23 aces and won 65 percent of the points when serving. He had 23 break-point chances and was able to finish off seven. Melzer lost just six points on serve in the decisive fifth set.
Russia will try to stave off elimination with veterans Nikolay Davydenko and Mikhail Youzhny against Austrians Oliver Marach and Alexander Peya in a doubles match Saturday.
Melzer meets Bogomolov and Haider-Maurer goes against Kunitsyn in singles matches Sunday.
Austria and Russia are in the same section of the draw as Spain and Kazakhstan. Spain grabbed a 2-0 lead in that series Friday. Series winners move to the quarterfinals April 6-8.