BUENOS AIRES, Aug 14 (Reuters) - Argentina's shock primary election leader Javier Milei, a radical libertarian economist, scored the largest share of the national vote with big wins in the provinces, breaking in some places decades of Peronist party domination.

Milei took 30% of the national vote, ahead of the main conservative opposition bloc Together for Change on 28% and the ruling center-left Peronist coalition on 27%. He won in 16 of the country's 24 regions, clicking with voters angry at 116% inflation and a painful cost of living crisis.

His out-performance sparked a sharp fall in the peso currency on Monday, with the central bank partially opening capital controls to let it slide nearly 20% to 350 per dollar before hiking interest rates to 118%.

Milei flipped nearly a dozen provinces won by the Peronists four years ago, stealing Santa Cruz for the first time since 1999, a symbolic win in the backyard of the powerful vice president and former two-term leader Cristina Fernandez de Kirchner.

Fernandez de Kirchner and her late husband Nestor Kirchner served as senator and governor of Santa Cruz respectively and her family has properties in the province.

Fernandez de Kirchner, the most influential political force in the Peronist movement for years, has seen her power wane as the government has grappled with triple-digit inflation, poverty hitting 40% and recurring debt crises.

The Peronist candidate for the 2023 election, Economy Minister Sergio Massa, hails from a more centrist bloc of the coalition and has not always seen eye-to-eye with the former president, who sharply divides opinion.

Alejandro Corbacho, director of the political science program at Argentine university UCEMA, said the primary vote was a rebuke to the Peronists generally, and specifically the left-wing around Fernandez de Kirchner.

"She is the person most responsible for this," he said. "Her political figure scares away votes."

Milei also flipped some traditionally important conservative provinces, including wine region Mendoza and central Cordoba. But he placed third in both the city and province of Buenos Aires, the country's major metropolitan center and its populous surrounding region.

Argentines will vote in general elections on Oct. 22, with Massa, Milei and former security minister Patricia Bullrich in a three-way split. If no candidate gets 45% or 40% and a 10-point lead, the top two will go to a second round in November.