Article by Sam Walker, The Wall Street Journal

High above Iowa, almost precisely 30 years ago, passengers aboard a United Airlines flight from Denver to Chicago felt an explosion. The tail engine had blown apart.

With its two wing engines still intact, the plane should have been able to land safely—but there was another, darker problem. Shrapnel from the blast had somehow severed not just one, but all three of the plane’s independent hydraulic lines, cutting all power to the flaps and rudder.

In the cockpit, the pilot asked the flight engineer to look up the procedure for steering a DC-10 under these circumstances. “There isn’t one,” he replied.

I often ask people what leaders they admire, and on several occasions, I’ve heard the name Alfred Haynes. He was the pilot of that plane.

Faced with a freak scenario (engineers had pegged the odds of a complete hydraulic failure at roughly a billion to one), the 57-year-old former Marine aviator put on a crisis-management masterclass.

Capt. Haynes spoke calmly and clearly to ground controllers and even thanked them for their assistance. At one point, when he was told he’d been cleared for an emergency landing on any runway at nearby Sioux City, he laughed. “You want to be particular and make it a runway, huh?”

Thinking quickly, he instructed one member of his three-man crew to grab ahold of the throttles controlling the two functioning wing engines. By carefully offsetting their thrust, the crew managed to direct Flight 232 down to one of those runways, but the odds were still against them.

The passenger jet was drifting side to side in a tailwind. It would have to land at 250 m.p.h., almost double the usual speed—and it had no brakes.

When the right wing clipped the tarmac, the fuselage slammed down, punching through a foot of concrete before flipping over and breaking into four pieces. Few witnesses expected anyone to survive—but miraculously, 184 of the 296 people on board were rescued.

Capt. Haynes suffered a bruised sternum, a concussion, 14 lacerations to his head and nearly lost an ear. But six days later, he was healthy enough to be wheeled into a press conference. “There is no hero,” he said. “There is just a group of four people who did their job.”

As I listened to Capt. Haynes cite the contributions of everyone involved, while saying nothing of his own, I thought of another famously self-effacing hero pilot, Chesley Sullenberger.

In 2009, after losing both engines on takeoff in New York and ditching his plane in the Hudson River without a single fatality, his first public comment was this: “We were simply doing the jobs we were paid to do.”

A similar scene had played out in 2010 when a Chilean mine caved in, trapping a group of workers. The hero of that ordeal was Luis Urzúa, the crew’s soft-spoken foreman, whose ironclad calm and quick thinking sustained his men’s lives and spirits for 10 weeks. The day they were rescued, he’d insisted on being the last man out. “Some things happened that—that weren’t the best,” he said. “But we learned how to keep our composure.”

Many of history’s most-celebrated leaders displayed a remarkable mix of courage and humility. But on the short list of leaders who’ve saved lives in the face of overwhelming odds, those two traits are nearly universal.

The reason, I suspect, is that they’re inextricably linked.

Few business leaders ever find themselves in the kind of fix where many lives hang in the balance. When they do, however, history suggests that a little humility can go a long way.

In 2014, for example, the newly installed chief executive of General Motors, Mary Barra, testified to Congress about a series of fatalities related to defective ignition switches. She surprised some observers that day by offering an unqualified apology. “I am not afraid of the truth,” she said.

Ms. Barra later won high marks for handling the crisis at GM and addressing what she called the “underlying cultural problems” behind it.

One prominent counterexample came in 2010 when BP’s Deepwater Horizon drilling rig dumped millions of gallons of oil into the Gulf of Mexico. Tony Hayward, the company’s CEO, drew fire for taking time off to attend a yacht race and for reportedly saying, “I’d like my life back.”

After stepping down, Mr. Hayward said he regretted making that comment but insisted he’d acted appropriately. “People find it easier to vilify an individual more than a company,” he said.

One widely cited example of corporate heroism involves Johnson & Johnson’s response to the 1982 Chicago Tylenol murders.

Although police quickly concluded the company wasn’t responsible for the poisoned bottles sold in stores, then-CEO James Burke didn’t hesitate to get involved. He directed his team to focus on protecting the public above all else. J&J pulled advertising, removed Tylenol from shelves and implored customers to stop using it—all at considerable expense.

The company later designed new, tamper-proof bottles without raising the price.

“I got a lot of credit,” Mr. Burke would say, “but there wasn’t anything else I could have done… The very soul of the corporation was watching us.”

Capt. Haynes, now 87, spent years giving talks about Flight 232 without accepting speaking fees. He described the miracle as a testament to luck, preparation and brilliant teamwork. He did not return calls seeking comment.

I’d argue that Capt. Haynes and these other reluctant heroes offer another lesson: Humility isn’t a byproduct of heroism, it’s a precondition. Modest people achieve miracles under pressure because they’re far more likely to possess four major qualities that pay dividends in a crisis.

1. Expertise

When the tiniest mistake can be fatal, there is no substitute for mastery. Before Sioux City, Capt. Haynes logged 7,000 hours in DC-10’s. Capt. Sullenberger, once a star Air Force cadet, had been flying for four decades. Mr. Urzúa’s 31 years of mining experience and extensive knowledge of topography proved invaluable to rescuers.

2. Composure

Heroes immediately grasp the severity of their problems and waste no time addressing them—all while maintaining ironclad emotional control. “You must maintain your composure in the airplane or you will die,” Capt. Haynes once said.

While Capt. Sullenberger later admitted to feeling “turmoil inside,” he said he never allowed himself to ponder his own fate. “I never thought about anything other than controlling the flight path and solving each problem in turn.”

3. Collaboration

Faced with an unprecedented situation, Mr. Urzúa understood that asserting his authority would only discourage others from making suggestions—so he promptly removed his white foreman’s helmet. “We are all equal now,” he told his men. “There are no bosses and employees.” From then on, every decision was subject to a vote.

Capt. Haynes often said he realized he didn’t know any more about landing that crippled plane than anyone else in the cockpit, and that many minds were stronger than one. “If we had not let everybody add their input, we wouldn’t have made it.”

4. Confidence

Heroic leadership often comes down to something simple: believing something so unequivocally that it becomes contagious. Rosa Parks, who set off a movement in 1955 by refusing to yield her seat on an Alabama bus, once said she’d learned “that when one’s mind is made up, this diminishes fear.”

Capt. Haynes said he never felt scared on Flight 232, but his true act of brilliance was his ability to project confidence. If the crew hadn’t believed they were going to make it, he said, “we couldn’t have operated.”

—Mr. Walker, a former reporter and editor at The Wall Street Journal, is the author of “The Captain Class: A New Theory of Leadership” (Random House).