Agnieszka Radwanska had got the Poles off to a hard-fought 1-0 lead with a 6-3 6-7 (9/7) 6-2 triumph over Eugenie Bouchard.
Earlier on Sunday, the Czech Republic had made a perfect start against Spain in Western Australia with world number six Petra Kvitova and veteran Radek Stepanek easing to their respective victories before they combined for a mixed doubles triumph.
Kvitova needed just 57 minutes to beat Anabel Medina Garrigues 6-1 6-0 while Stepanek beat world number 194 Daniel Munoz-De La Nava 6-2 6-2.
The result gave the Czech Republic an unassailable 2-0 lead over Spain ahead of the mixed doubles rubber which Kvitova and Stepanek won 6-3 6-4.
Panfil though dominated in the evening and in quotes reported on the official Hopman Cup website, he said: "I'm really surprised, it was my best match in my career so I'm really happy and back into Australia after six years.
"I'm really happy to be here, I still can't believe it.
"I was so, so focused on every point. I was serving really good, much better than yesterday ... I was trying to play like always my best tennis. The serve's were pretty good and my forehand as well."
On the back of an easy win over Flavia Pennetta on Saturday, Radwanska's testing encounter was the perfect preparation ahead of the Australian Open.
'I think so, yes of course, I think every match is a great practice between playing points and playing a real match. [It] is a great warm-up before Sydney and Melbourne. So I'm very happy I could play another good match and I'm ready for the next one," the world number five said.