Ukrainian captain Mikhail Filima's decision to alter the singles clash came as a shock given world No. 883 Lyudmyla Kichenok pushed Australian star Ash Barty in three sets on Saturday.
But the late ring-in still had Gavrilova looking troubled as the Australian looked to bounce back from her opening day "shocker".
It took plenty of grit but Gavrilova clinched the first set before Kichenok stormed back into the contest with a dominant second set.
Gavrilova fended off two break points in the deciding set but frustrations boiled over and left her in need of a new racquet as Kichenok served to level the tie.
Ash Barty's comprehensive victory over rising star Marta Kostyuk meant Australia's fortunes hinged on a Gavrilova triumph.
Barty says the Australian team didn't need to rally around Gavrilova, confident the 23-year-old would be able to find form in her second stint on court.
"She was disappointed, that's no secret, she was disappointed with the way things went out on court but she's also very, very good at moving on."
Ukraine's late change even caught Kostyuk by surprise before she opened the day in a straight sets loss to Australian No. 1 Barty.