About five years ago, the Los Lonely Boys experienced the thing most bands dream of but never achieve: a hit single.

“Heaven” is one of those radio-friendly pop-rock hits with plenty of shelf life — enough that, five years later, major stations still have it in regular rotation. For most of us, “Heaven” was our first introduction to the group, which will perform an acoustic concert Sunday at the Verizon Wireless Center. But Jojo Garza, one of the three Los Lonely brothers, said the success was far from overnight, nor was it something they banked on in order to feel successful or happy.

“We’d been playing since we were 7 or 8,” he said of his brothers, Henry and Ringo Garza. “We worked really hard all our lives.”

The national mainstream exposure that song afforded them wasn’t something they had ever planned on. They were paying bills by playing anywhere they could and making sure they had enough money to put food on the table. “Heaven” certainly made that easier, Jojo admits.

“We never really said, ‘We’re gonna do it (get famous),’” said Jojo, bass player. “It was more like, ‘Could you imagine if we were there and had all those lights and all the people screaming and all the girls screaming and all that stuff?’”

The biggest influence on the Garzas, of San Angelo, Texas, was their father, Ringo Garza Sr., who played in a band with his brothers in the 1970s and 1980s in southern Texas called The Falcones. The band, itself, wasn’t so much an influence, Jojo said, but their father taught them how to play all their instruments and encouraged them to be musicians.

Over the years playing together, the sound they developed — rock mixed with blues, soul and country — they coined as Texican rock ‘n’ roll in honor of their home state.

“People kept asking us to categorize our music,” he said. “It was pop and rock and country and funky, so we just decided to call it Texican.”

The Los Lonely Boys began playing professionally in Nashville in the 1990s. But they didn’t record their first album until they moved back to Texas. They recorded in Austin in Willie Nelson’s Pedernales studio. The self-titled album was purchased by Epic Records in 2004 and released, as was their single, “Heaven.”

“Heaven” went to No. 1 on the Adult Contemporary chart and No. 16 on the Billboard Hot 100. The single experienced success on the country charts as well, and was featured in the Guitar Hero On Tour. The band won a Grammy Award for Best Pop Performance by a Duo or Group with Vocal in 2005. Their other songs, “More Than Love” and “Onda,” also were nominated for Grammys in 2006.

The albums “Sacred” and “Forgiven” came out in 2005 and 2008, respectively.

The most recent news revolves around the release last week of “1969,” a five-song EP of all covers and the group’s first release on their new label, Playing in Traffic, and their own imprint, Lonely Tree. Each of the songs were originally recorded in 1969, and the band covered them as a celebration of the 40th

anniversary of “one of history’s most fabled years.”

The songs include: Santana’s “Evil Ways,” The Doors’ “Roadhouse Blues,” Blind Faith’s “Well All Right,” The Beatles’ “She Came In Through The Bathroom Window” and Tony Joe White’s “Polk Salad Annie.”

The band’s manager had been digging up a lot of old music from that year and brought the idea for the EP to the guys. Despite not even being alive in 1969, Jojo thought it was a good idea.