In a perfect world, the road to success would read like a fairy tale: Boy starts band. Band signs record deal (becomes huge in Japan). Fame, women, luxury ensue.

But the world is far from perfect, as Billy McCarthy, lead singer of the Brooklyn band We Are Augustines, would likely concede. McCarthy, along with bassist Eric Sanderson and drummer Rob Allen, told his more complicated story, a real and epic tragedy of battling the odds and still standing tall, during the band’s Sunday night’s show at Red Palace.

McCarthy has had a rough go of things. He grew up in foster care in rural California and never knew his father. His mother, a diagnosed schizophrenic, overdosed on painkillers and cocaine when he was a teenager. Some years later, his brother, James, also a schizophrenic, hanged himself after learning he was to face a lifetime of solitary confinement in a mental institution. Shortly after McCarthy returned from a trip to the West Coast to collect James’s belongings, McCarthy’s first band, Pela (of which Sanderson was a member), fell apart unglamorously after nearly a decade.

McCarthy and Sanderson hung together, though, and pushed forth as a duo. After two more years of fruitless meetings with industry executives, their debut album, “Rise Ye Sunken Ships,” was released independently in June.

The album is good. Very good, even. But the band — live, with the help of new addition Rob Allen on drums — is extraordinary.

For skeptics: This is not a sympathy vote. McCarthy’s story is relevant because it is precisely what makes him so powerful. Rather than wallow in the past, the band casts for redemption, treating each confessional track as a lesson in perseverance. As it rolled through minor chord progressions, military-like drumming and McCarthy’s severe yet supple wail, Sunday’s routine felt almost therapeutic, like an attempt to process the pain before leaving it behind.

To the eye, they were dreamy, rough-around-the-edges rockers, with the mysterious McCarthy in particular effusing a masculinity and grit so earnest, you’d buy that he’d spent the night in a steel mill draining whiskey. Tender yet tough, his bashful, infectious grin had female fans blushing.

The heat only intensified when he took the stage solo for a few slower numbers, including “Juarez” and a heart-wrenchingly humble cover of Tom Petty’s “Even the Losers.” His voice, syrupy and worn, drifted between the grainy chill of Kings of Leon’s Anthony Followill and the creamy soul of Ray LaMontagne.

McCarthy’s brooding presence was countered by the vivacious Sanderson, who served as a sunny liaison between the band and audience. And Allen surpassed both partners in energy. Sans microphone, he stormed through bar after bar, howling at his drum set.

There is purity here, a raw authenticity that bonds these three wise men.

“The message we want to send as a band is just, hang in there . . .” McCarthy said, strumming the opening chords to “Augustines.” “If we can do it, I think, well, pretty much anybody can do it.”

Then came “Chapel Song,” one of the band’s catchiest numbers, which recalls McCarthy watching a lost love marry another man: (“I’m a bowl of bruised fruit / Inside a chapel of shiny apples / Tear up the photograph / ‘Cause it’s a bright new sky”).

A homage to the past or an ode to new frontiers? Likely both. This is a band not only on the mend, but on the rise. And this could be just the beginning.