With the Australian Open just over a week away, Bouchard said she didn't think her injury was serious.
"I played great throughout the three sets and Sasha probably dropped his level a little bit in the second and third sets", he said.
Elise Mertens beat Canada's Eugenie Bouchard 6-4 6-4 to hand Belgium the advantage and David Goffin sealed the tie for the European side with a 6-2 6-4 win over Vasek Pospisil. "I don't think it's too bad".
The third set was nearly as one-sided as the second as the world number two lost just two games in sealing victory to give his country the lead in the final.
The world number four won the first set 7-5, but Kokkinakis rallied back in a big way in the second.
Two-time Grand Slam singles champion Angelique Kerber beat Australia's Daria Gavrilova 6-1, 6-2 to put Germany one win away from a Hopman Cup final against Roger Federer and Belinda Bencic of Switzerland.
Kokkinakis and Gavrilova lost their mixed doubles showdown against Zverev and Kerber 1-4 4-1 4-3.
Zverev praised two-time major victor Kerber's performance, admitting he nearly lost the match for Germany.
Zverev came out all guns blazing in a high-intensity first set where both players produced moments of brilliance, with both holding multiple break points. I'm going to the physio now to see what it is. "I didn't play my best today - luckily I have an unbelievable partner".
Germany has defeated Australia to qualify for tonight's Hopman Cup final against Switzerland.