Mr Burke has demanded Mr Joyce be suspended from cabinet and abstain from votes in Parliament while his citizenship of New Zealand and eligibility to be an MP is considered by the High Court.
The reactions to her sweet, sweet revenge have been just as good.
Both the Greens - which have lost two senators over dual citizenship dramas - and the Labor Party have called on Mr Joyce to resign as Deputy Prime Minister until the High Court rules on his case.
"Not since the old days of worrying about Soviet Russia, that is how long since we have had to worry about these sort of things", he told Sky News.
On Tuesday, Heard took to Twitter and had some fun at the expense of Australian Deputy Prime Minister Barnaby Joyce.
This country's own farcical few weeks notwithstanding, there will be many New Zealanders looking on in glee at the developments, given our often rivalrous relationship.
You can check your citizenship status here.
Australia's High Court will begin hearings into Joyce's eligibility on August 24.
Not in touch with Congress MLAs: Vaghela
Ahmed Patel , who today met Congress MLAs after they returned from their Bengaluru sojourn, said he was confident of his victory. The Congress has the strength of 51 in the House but it can not bank upon the seven MLAs who refused to go to Bengaluru.
But on Tuesday a number of government ministers implied the New Zealand Labour Party had colluded with the Australian Labor Party to bring down Australia's government.
Yesterday, Joyce became the latest in a string of sitting politicians to be rocked by revelations of dual-citizenship with other countries, which is grounds for immediate disqualification from Federal Parliament, under section 44 of the... y'know...
The unlikely dispute involved Barnaby Joyce, Australia's deputy prime minister.
"From my perspective, we've made it clear it shouldn't have happened but ultimately it was questions raised by the media that caused this situation, rather than questions from us", she said.
But Labor is resisting demands it produce proof that none of its MPs have dual citizenship, claiming its candidate vetting processes prevent any dual citizens from slipping through the cracks.
But now it is out in the open, it is highly likely the citizenship clause will trap even more Australian politicians on all sides of parliament, Economou said.
"But I think as heads cool down and they get on and resolve the issues around Barnaby Joyce then we can get on with the positive relationship because that's what we need to do in the best interests of New Zealand".
He argued the court "will so hold" Joyce's right to sit in parliament.
Following that, One Nation senator Malcolm Roberts was discovered to be a dual citizen with England at the time of his election, which would render him ineligible to be elected.
"Assuming this passes his biosecurity laws", Heard quipped.