A win in one of the three remaining matches in the series would boost Kazakhstan into the quarterfinals in April.
Golubev had one break in each set but also dropped serve once in the first and third sets, forcing the tiebreakers. He was good on just 54 percent of his first serves but won more than 90 percent of the points on his second serve.
Golubev had 15 aces and 48 winners but also had to overcome 70 unforced errors, figures indicative of aggressive play.
Korolev had 53 winners in getting past Melzer. He won nearly half of the points off Melzer's serve and cashed in six of his eight break opportunities.
Golubev is to return to the court Saturday, teaming with Yuri Schukin for a doubles match against Austrians Julian Knowle and Alexander Peya. Sunday's schedule calls for reverse singles with Golubev taking on Melzer before Korolev plays Haider-Maurer.
The winner of the Austria-Kazakhstan series will go against the winner of a weekend series between the Czech Republic and Switzerland.