The Mavericks’ 2013 performance at the New Orleans Jazz and Heritage Festival knocked out a huge crowd at the Gentilly Stage. It’s rare for a national act to appear at Jazz Fest two consecutive years, but the Mavericks are back in 2014, playing Saturday at the former Gentilly Stage, now the Samsung Galaxy Stage.

Originally from Miami and now based in Nashville, Tenn., the Mavericks play an infectious montage of classic rock ’n’ roll and pop, traditional country and Cuban and Tex-Mex rhythms. Possibly last year’s most talked about Jazz Fest act, the band’s delighted listeners included Jazz Fest producer-director Quint Davis.

“I’d never seen the Mavericks perform before,” Davis said in January when the 2014 Jazz Fest lineup was revealed. “They blew me away.”

Wanting more Mavericks, Davis attended the Mavericks’ October show at Tipitina’s and personally invited the group to return to Jazz Fest.

The Mavericks had Jazz Fest on their wish list of gigs for years.

“Jazz Fest is so notable,” multi-instrumentalist Robert Reynolds said recently. “Everybody recognizes Jazz Fest for what it is — very special.”

Reynolds attended Jazz Fest for the first time in 1990. Mavericks drummer Paul Deakin’s parents lived in New Orleans at the time. A Jazz Fest engagement for the band, however, didn’t materialize until the band’s 24th year of existence. The Mavericks’ festival debut did not disappoint them. During the show, singer Raul Malo told the audience, “We’ve dreamt our whole lives of coming here. We don’t care if it’s rainy and muddy!”

“I watched something happen from the stage that day,” Reynolds recalled. “To my eyes, it was a phenomenon. I saw maybe 2,000, 3,000 people enduring less-than-pleasant weather. The crowd grew to 5,000 and then, what appeared to me, 10,000 or 12,000, a heaving mass of people enjoying the band.

“The crowd grew in front of our eyes, and the band grew with it. We took that journey together. When we left the stage that day, it felt like something had happened. It felt like the thing you aspire to but you can’t always get. You only hope to get it.”

The Mavericks’ latest Jazz Fest appearance comes in the band’s 25th anniversary year, during its “Twenty-Five Live” tour.

The members of the Mavericks, which was formed in south Florida, started getting to know one another in 1989, then began rehearsing in the late summer of that year. The group played its first show in December 1989. By 1990, the group was busy.

The Mavericks’ self-titled, independently released 1990 album grabbed the ears of Nashville-based record companies. The group signed with the MCA in 1991. The band’s commercial success began in 1994 with the hit “What a Crying Shame,” featuring lead singer Malo’s emotional, Roy Orbison-like vocals. Subsequent U.S. success included “O What a Thrill” and “There Goes My Heart.” Another song, “Dance the Night Away,” was a hit in the U.K.

Following Malo’s parallel solo career and membership in super group Los Super Seven, the Mavericks went on hiatus in 2004. The break lasted eight years.

“That’s a long time,” Reynolds said. “There was a period there when I began thinking, ‘Well, what if we don’t return to this?’ But I always thought, ‘You don’t leave something that’s been so important to you. You’ll find the time to come back.’ ”

The Mavericks regrouped in 2012. They released their much-acclaimed reunion album, “In Time,” last year.

“In our purest, truest heart, we are celebrating 25 years,” Reynolds said. “We don’t have a new album in our 25th anniversary year, but there’s new music in the pipeline. Raul has created great new songs, and the band is excited to be onstage every night.”