Sabalenka beat Golubic in just over two hours to give Belarus an unassailable 3-1 advantage in Minsk.
Sabalenka, who is 125th in the world, won 6-3, 2-6, 6-4 in her first ever meeting with Golubic, 54 in the world, in just over two hours to give Belarus an unassailable 3-1 advantage in Minsk.
"I gave everything I had for this win," Sabalenka said. "This is the first major victory in my career. Hopefully it will not be the last one."
The Belarus teenager looked in command at the start as she produced an early break and kept her narrow lead for a one-set advantage after 39 minutes against the 24-year-old Golubic.
Golubic stepped up a gear in the second set, breaking her rival's serve on three occasions to level at one-set all after one hour 14 minutes on court.
In the deciding set the opponents traded breaks early before Sabalenka grabbed the deciding break in the ninth game.
Earlier on Sunday Aliaksandra Sasnovich put Belarus into a 2-1 lead as she upset Timea Bacsinszky in straight sets 6-2, 7-6 (7/2) in one hour 35 minutes at the hard courts of Minsk Chizhovka arena.
"I was well prepared for this match both mentally and physically," Sasnovich said. "I played well today and I'm very glad to win the second point for my team. Belarus tennis now have a historic chance."
In the Fed Cup final Belarus will face either Czech Republic or the United States, who are tied at 1-1 after the first day.