Drawn up by Australian officials, the map is the latest weapon in the country's campaign to convince its Asian neighbours that it is not really Down Under, or off the map entirely, but one of them.
"The East Asian Hemisphere is where we live," Mr Evans told the seven foreign ministers of the Association of South East Asian Nations (Asean), whose annual conference in Brunei wound up on Thursday night.
"This is where we have to find our security. This is where we can best guarantee our prosperity. This is where not only our neighbours are, but our closest friends."
The map which Mr Evans flourished showed Australia in the centre of a region bounded by Siberia to the north, Antarctica to the south and Burma to the west. Spanning the area in between were Japan, China, Korea and the booming "tiger" economies of South East Asia, with which Australia's Labour government has adopted a policy known as "comprehensive engagement". New Zealand just made it on the map in the far east.
Mr Evans's definition of the East Asian Hemisphere, and of his country's place in it, evoked surprise, followed by indignation. Malaysia, the Asean member with the most prickly relations with the West - and one which has had a rocky relationship with Australia - resented Mr Evans's attempt to rewrite the regional map.
"If I look at a map, I believe that it says that Australia is not part of Asia," said Abdullah Ahmad Badawi, Malaysia's Foreign Minister.
"We are part of Asia, and Australia is down there. Australia is another continent."
Why, asked an Indonesian journalist, was Australia so determined to become part of Asia when it was a "white race" down south?
Such remarks brought forth a bristling reply from Mr Evans, who has worked tirelessly in his seven years as Foreign Minister to strengthen Australia's image in Asia
"It is a little crude, with respect, a little out of date, to make the sort of assumption that there is something fundamentally different between Australia and New Zealand and the countries to our north," he said.
But is it? The dilemma which the Asean-Australia spat re-opened lies at the heart of Australia's attempt to recast its identity as a country breaking free from its European past and forging a future as leader of the Asia-Pacific region.
Australia's wish to bridge the cultural divide and become a regional leader has been a driving force behind its republican movement and the campaign against France's planned resumption of nuclear tests in the Pacific.
The roots of the identity conundrum run deeper. This week, Australia has been marking the 50th anniversary of the founding of an immigration policy which has transformed it from an Anglo-Celtic country to one of the world's most diverse multicultural nations, now taking almost half its immigrants from Asia. The founder of that policy, the late Arthur Calwell, a Labour government minister, never intended it to evolve in this way. A defender of the discredited White Australia policy, he once made the infamous remark: "Two Wongs don't make a White."
As late as 1972, Mr Calwell said: "If Australians are ever foolish enough to open their gates in a significant way to people other than Europeans, they will soon find themselves fighting desperately to stop the nation being flooded by hordes of non-integrables."
Some Asian leaders see such sentiments still lurking below the surface of Australia's national psyche. For their part, Australian officials grumble that the insular regional view promoted by countries such as Malaysia is little more than a reverse mirror image of the old White Australia policy.
It was Malaysia that vetoed a move at the Asean conference this week to admit Australia and New Zealand as participants in the inaugural summit of Asian and European leaders due to be held in Thailand early next year. The Asean ministers eventually agreed to Australia and New Zealand joining the second Asia-Europe summit in 1997. The question of which hemisphere the two countries will represent is still open to dispute.