Three years later, when it went on sale, the automotive press couldn’t believe their stopwatches. Not only was this the most breathtakingly futuristic rolling sculpture anyone had ever seen—it was the fastest production car they’d ever tested.

Road & Track said of Lamborghini’s Countach: “Its no-holds-barred, cost-no-object design is, on one hand, one of extremes and excesses and, on the other hand, a mobile demonstration representing the pinnacle of automotive design, technical achievement and sophistication, the likes of which we will probably never see again.”

Business leaders who aspire to build revolutionary products usually consult the same handful of case studies: Apple ’s iPhone, Nike ’s iconic waffle sneaker treads or Pixar’s breakthrough animated films. Along the way, they invest millions in market research, hire large teams of veteran engineers and helicopter-parent the project.

To build the Countach (KOON-tash), a car that changed the course of automotive history and appeared on the bedroom walls of millions of besotted adolescents (including mine), Mr. Lamborghini did exactly none of those things. He simply rounded up three precocious 30-somethings, gave them a clean sheet, ordered them to build the maximum car and left them alone.

It’s not surprising that business schools ignore this story. The Countach never made anyone a billionaire despite its $52,000 original price tag ($296,000 in current dollars). Over 16 years, the chronically troubled company took many more orders for the car than it managed to fill; in all, only 2,049 were made.

What really emerges from the hodgepodge of books, trade articles and firsthand accounts of the Countach’s construction is a counterintuitive model for leading a team toward genius. Signor Lamborghini’s brilliance lay in creating the ideal conditions for something magical to happen.

The Countach took its name from a Piedmontese slang expression one enraptured worker reportedly blurted out upon seeing it for the first time. Loosely translated, Countach means “holy s---.”

The bodylines were the work of Marcello Gandini, a 31-year-old designer from the Italian style house Bertone, who’d drawn the shapely curves and eyelashlike headlamp accents of Lamborghini’s Miura. Like most sports cars of the era, the Miura gave off a distinctly anthropomorphic vibe. The Countach would put an end to all that.

Inspired by a space-age prototype he’d penned for Alfa Romeo, Mr. Gandini drew a low-slung, angular, muscular body with a nose that narrowed to a wedge. He pushed the cabin forward, added insectile doors that swung dramatically upward and used hexagons to give its body panels a mathematical logic.

This menacing design would turn Mr. Gandini into a superstar, but that was only half the battle. The Countach also had to be fast—and roadworthy.

Paolo Stanzani, the 33-year old engineer tapped to build the car’s mechanical underpinnings, knew it would be difficult to fit a hulking V-12 engine behind the driver in a space only 42 inches tall. For better weight distribution, he mounted the engine backward with the output shaft in front.The chassis he commissioned was a handbuilt one-of-a-kind tubular spaceframe—itself a work of art.

The crucial job of refining the Countach fell to the third team member, Bob Wallace, a 32-year-old New Zealand-born test driver. Mr. Wallace wanted to avoid a flaw in the Miura, whose aerodynamics had made it unstable at high speed, but didn’t have access to a wind tunnel.He resorted to gluing strands of cloth to the body and filming them at speed to measure airflow.

As his team worked, Mr. Lamborghini mostly let them be. When he did check in, it was usually to express skepticism about whether the Countach would actually work. Before agreeing to put the car into production,he ordered Mr. Wallace to ferry it to an endurance race in Sicily and return it to the factory with the engine still running.

The Countach wasn’t perfect—or practical. Climbing in and out was a struggle, rear visibility was virtually nonexistent and there was no room for a proper suitcase. After Mr. Lamborghini was forced to sell a controlling stake in the car maker in 1973, subsequent owners debased it with garish side skirts, fender flares and a colossal rear wing.

Nevertheless, the Countach’s legacy endures. The original “periscopio” model that caused pandemonium in Geneva now fetches more than $1 million at auction. Seeking inspiration in the 1990s, General Motors borrowed a Countach, blindfolded a group of designers and let them fondle its bodylines with their bare hands.

There’s no question that the Countach contributed to Lamborghini’s renaissance under its current owner, Volkswagen’s Audi AG. The brand is currently working on an electric supercar.

Sometimes, future-altering products are works of a singular genius. Other innovations, such as the iPad’s multitouch screen or the aperture grilles inside Sony ’s 1968 Trinitron color television, draw on years of tireless research. Recent studies suggest companies can achieve consistent gains by soliciting lots of small innovative ideas from employees.

What the Countach really offers is a counterpoint to the Steve Jobs model: the notion that a team leader who inspires genius must be a hard-driving visionary who relishes getting into the weeds.

The late Harvard psychologist Richard Hackman, who studied many kinds of effective teams, found that once the actual work began, team leaders had limited impact. What mattered most were the intelligent preparations the leader made beforehand.

Ferruccio Lamborghini might have gotten lucky with the Countach, but there’s no question that he set a favorable stage. He’d built a capable factory and a brilliant engine and infected his workers with high standards. His finest achievement, however, was identifying three emerging talents with fresh eyes who weren’t married to the status quo. He simply told them to build something incredible—then went waterskiing.

The hard work of leadership was already done.

Write to Sam Walker at sam.walker@wsj.com