Melzer, the world number 15, reached the semi-finals at the French Open last month, where he lost to Rafael Nadal, and also tasted success in the Wimbledon men's doubles event alongside Germany's Philipp Petzschner.
"It's brilliant, I'm really happy," said Golubev, the world number 82.
"I've played extremely well this week."
The 23-year-old's best previous result at an ATP tournament was a runner-up finish at the St Petersburg Open in 2008.
"He hits the ball hard and when he hits it well, he's difficult to beat," said Melzer.