Twenty-five years ago, few Argentines would ask a bartender for a fernet—with its dark-caramel color and black-liquorice nose—mixed with Coca-Cola. Today, however, they seem to order little else. And nearly all of the time, they order just one brand: Fernet Branca.

Behind the spectacular rise of fernet is, for many, one of the most successful marketing strategies in Argentina’s recent history.

Perhaps even more remarkable is the continued dominance of Fernet Branca, which has cornered more than three quarters of the market and been embraced by Argentines as a national symbol.

“People here think that fernet is Branca,” said Agustín Camps, an Argentine marketing consultant for the food and drinks industry.

The waves of Italian immigrants who began arriving in the late 19th century brought fernet and a host of other cultural idiosyncrasies to Argentina. But until the 1990s, fernet was just a mildly popular digestif or aperitif. Doctors sometimes recommended it as stomach medicine; older people added a drop to their dessert coffee.

In 1990, producers in Argentina could satisfy demand with about 1 million gallons of fernet, according to the national chamber of distillers. By 2013, though, the nation’s output had rocketed to 14.8 million gallons. (That’s 75% of the world’s fernet, according to IWSR, a wine and spirits market research firm based in London.)

The shift was driven by Fratelli Branca, a leading producer from Milan that opened its Argentine subsidiary in Buenos Aires in 1941.

“If you come to understand what we did with the product, you’ll understand what a revolution is,” said Hernán Mutti, 68, head of marketing at Fratelli Branca since 1992.

Indeed, family-run Fratelli Branca’s success at selling fernet has been compared to Smirnoff vodka’s push in the United States during the late 1940s. Mutti and his colleagues took fernet from a fusty digestif sipped neat to Argentina’s national drink—like rum in Cuba—mixed in large volumes with Coke at weekend barbecues and nightclubs.

And despite being more expensive than its rivals, Fernet Branca is preferred by people of all social classes.

“Fernet is Branca,” said Juan Piedrabuena, 23, a brickmaker who was sharing a pint of fernet and Coke with friends at a folkloric music event. “The others aren’t the same.”

Around 1990, Fratelli Branca began promoting the marriage with Coke—whose sweetness counteracts the sharp bitterness of fernet—with tasters at bars, sporting and cultural events, and popular beach towns along the Atlantic coastline. The target market was people under 25, whose perceptions of fernet were untarnished.

“We had to convince Argentina that this was the way to drink fernet: to be shared between friends,” Mutti said. “It was being drunk behind close doors; it wasn’t a friendly product.”

The tasters were accompanied in the mid-1990s by advertising that sought to tie Branca to distinctive landscapes, like the Perito Moreno glacier in Patagonia. This strategy would lead to the slogan used on billboards today: “Unique.”

As fernet’s popularity surged, Fratelli Branca expanded, opening a new plant outside Buenos Aires 15 years ago, where fernet matures for a year in giant oak barrels. And Argentina began to ponder a rising national symbol.

“I’d venture to define fernet as an anecdote in the creases of Argentina’s nascent modernity,” Diego Vecino, a social commentator, wrote in a 4,000-word magazine piece that explored the new cultural importance of fernet, “Imperfect, proletarian, aggressive, with a history of trans-Atlantic pilgrimage.”

(Fernet has gained a devout following in at least one other city outside Italy. In San Francisco, it became en vogue among bartenders, who would drink a dram, perhaps followed by a ginger ale chaser, before it won broader appeal.)

The ritual surrounding fernet is as important as the drink itself. In the past, customers requested a “90-2-10,” which meant one tenth of fernet, nine tenths of Coke and two ice cubes.

But today, most people use far greater proportions of fernet, sometimes up to half. Nico Tilli, 23, a dentistry student, said he counts 12 seconds from when the first drop of fernet hits the bottom of the glass. He then adds a dash at the end to tame the sepia-colored froth.

In recent years, other fernet brands have emerged, like 1882, distilled by Porta Hermanos in Córdoba, a city 430 miles west of Buenos Aires where fernet is hugely popular.

The company toiled for years to create an infusion specifically for mixing with Coke, then hired top branding experts like Fernando Moiguer to develop a marketing strategy that tapped into local pride.

“They told us we were crazy,” said Inés Castro, 55, Porta Hermanos’ head of marketing. “Branca was like a god in Argentina.”

In 2014, Fernet Branca had 79% of the market, according to IWSR. Two other products on Fratelli Branca’s fernet line had another 11%. Of the rest, just 3% went to 1882.

“It’s like David and Goliath,” Castro said. Still, Porta Hermanos is moving to expand, she added. They’ve teamed up with Cepas, a drinks company that has better distribution, and together they recently tested a ready-mixed fernet and Coke drink.

Some entrepreneurs are trying other ploys to break into the market.

Hernán Vecchioni, a food engineer in his thirties, launched a new micro-distilled fernet last year called Nero 53. He said it was impossible to match the broad appeal of Branca. Instead, Mr. Vecchioni’s four-man business targets a yuppie clientele, and markets Nero 53 as a “boutique” fernet for drinking neat in tony bars.

After Argentina’s economy began to stumble a few years ago and consumption of beer slumped, fernet continued to thrive, according to figures compiled by Abeceb, a local economic analysis company. This resilience is a powerful demonstration of how cultural phenomena can defy the prevailing economic winds, analysts said.

Still, in the last couple of years fernet has also suffered the effects of high inflation, which curtails purchasing power, and consumption waned a little for the first time in a decade.

Competition has also emerged from Campari, another traditional Italian bitter aperitif that Argentines mix with orange juice. But Fratelli Branca is fighting back; it has recently begun to promote mixing fernet in a new cocktail with a touch of syrup and ginger ale. Still, the mix with Coke seems safe for now.

“We need to diversify consumption,” Mutti said. “But we’re not going to abandon the thing that made us the market leader.”