The Pacific Islanders, forced to play as Tonga Invitational XIII due to political infighting, beat the Lions 14-6 in Hamilton last month before pulling off a stunning 16-12 defeat of the world champions at Eden Park on Saturday.
New Zealand, Great Britain and England were the only sides to have beaten Australia in the previous 41 years before their stunning loss to Kristian Woolf's side.
The Tongan team have been invited for an official reception in recognition of their victories and they will be even more popular after a national holiday was declared.