Usually the countries that dominate international sports competitions are the ones more populated than New Zealand, which has just 4.6 million people. Yet the island nation is competing, and winning, in a whole range of sports. Its next task: winning the Cricket World Cup.

On Tuesday, New Zealand’s men’s cricket team beat its counterpart from South Africa, a nation of more than 54 million, to advance to its first cricket World Cup final. (And they did it in a thrilling match.) New Zealand has won all eight of its games in this year’s competition, and is the country with the smallest population to ever reach the title match in the competition’s four-decade history. The last World Cup champion, India, had just a slightly larger population: 1.28 billion.

Winning any World Cup is a big deal for such a small country. After all, my friend Stephen Wells, a London-based photographer, told me, “Any international/global achievement no matter how trivial is a big deal in NZ.” He added, “Some of us have an inferiority complex that we’re an afterthought of a country, because sometimes we really are an afterthought of a country. But not now.”

If the Kiwis beat their neighbors, Australia, on Sunday in Melbourne, New Zealand will become only the second country ever to hold the World Cup titles for both men’s rugby and men’s cricket at the same time.

As good as New Zealand is in cricket, it’s better in rugby. The men’s team won the last World Cup, in 2011, its second. It has a winning record against every team it has ever played, has been ranked No. 1 for longer than all other teams combined and is the betting favorite to defend its title at this fall’s World Cup. New Zealand’s two rugby World Cup triumphs are the only wins in either World Cup in the last 35 years by a nation with fewer than 5 million people.

YEAR SPORT WINNER POP. RUNNER-UP POP. 1975 Cricket West Indies 4.6m Australia 13.9m 1979 Cricket West Indies 4.8 England 46.7 1983 Cricket India 748.0 West Indies 5.0 1987 Rugby New Zealand 3.3 France 56.0 1987 Cricket Australia 16.3 England 47.3 1991 Rugby Australia 17.3 England 47.3 1992 Cricket Pakistan 117.3 England 48.0 1995 Rugby South Africa 41.4 New Zealand 3.7 1996 Cricket Sri Lanka 18.4 Australia 18.3 1999 Cricket Australia 19.0 Pakistan 140.6 1999 Rugby Australia 19.0 France 58.9 2003 Cricket Australia 20.0 India 1,093.8 2003 Rugby England 49.9 Australia 20.0 2007 Cricket Australia 21.2 Sri Lanka 20.3 2007 Rugby South Africa 49.6 England 51.4 2011 Cricket India 1,210.2 Sri Lanka 20.9 2011 Rugby New Zealand 4.4 France 63.1

New Zealand also has won one World Cup in women’s cricket and finished second at another. And it won four of seven World Cups that have been held in women’s rugby.

Again, all that with fewer than 5 million inhabitants.

These achievements might be easy to dismiss if you’re not into cricket or rugby. The sports have widespread but not worldwide appeal. Mostly they’re limited to former British territories and Commonwealth countries, and neither is yet an Olympic sport. But New Zealand has done well in the men’s soccer World Cup lately, too. It qualified in 2010 — as the third least populous country, bigger only than Slovenia and Uruguay — and was the only team not to lose a match. (It drew all three of its group-stage matches and was eliminated.) It fell one game short of qualifying for last summer’s World Cup. The women’s team qualified for the 2007 and 2011 women’s World Cups.

In the Summer Olympics, New Zealand has been gaining on its more populous rivals. It won 13 medals in London in 2012, the fourth straight Summer Games in which New Zealand increased its medal total. It ranked seventh in per-capita medals in 2008, and fourth in 2012, behind only nations that won all their medals in athletics. New Zealand athletes medaled in six different disciplines in London.

“That shows there’s a system in place, not just chance or concentration on one sport,” said Alex Baumann, chief executive of High Performance Sport New Zealand, the government body that sponsors recreation in the country, in a telephone interview earlier this month.

Baumann attributed the country’s sporting success to a number of factors. As with many things, it starts with money. Over the last five years, the government has increased its investment in his department by nearly 50 percent.

“In the end, we don’t have all the resources like other countries do, like the U.K. or Australia or even Canada,” Baumann said. “You can’t spend the resources so thinly that you don’t make the difference.”

Prioritizing funding has spurred individual sports federations to excel, not just for glory but to keep getting money from the government. “There’s that kind of tension between sports to do well,” Baumann said.

That philosophy, and a deep emphasis on sports, is shared by Australia, New Zealand’s close neighbor and ally and sporting rival. While New Zealand lately has topped the standings for sporting performance by countries with fewer than 5 million people, Australia has been the dominant global sports force for countries with fewer than 20 million people. Baumann pointed out that each country’s prime minister attended the cricket teams’ World Cup match last month in Auckland, even though it was in the group stage and unlikely to eliminate either team. “It highlights the importance of sport,” Baumann said.

CORRECTION (March 27, 3:03 p.m.): An earlier version of this article said India won the cricket World Cup last year. It won the last cricket World Cup, in 2011.

CLARIFICATION (March 27, 3:32 p.m.): A previous version of this article said the cricket World Cup final will be played on Saturday. Its scheduled starting time is 2:30 p.m. on Sunday in Melbourne, which is 11:30 p.m. EDT Saturday.