Few bands in the history of pop music have been as misunderstood as Spandau Ballet has been in America.

The British quintet, known mainly for its synth-soul ballad “True” and the gloriously off-kilter anthem “Gold,” has long been seen as an ‘80s oddity, cultural shorthand for an intensely cherished trend that falls out of favor.

Spandau Ballet hasn’t exactly helped matters by limiting its appearances here. However, with its Beacon Theatre concert Saturday night, part of the band’s first American tour in 30 years, that could all change. (The band plays NYCB Theatre at Westbury Sunday night.)

Between the band’s new documentary “Soul Boys of the Western World,” which hit theaters last week, and this two-hour mix of nostalgia and reinvention, Spandau Ballet shows not only how it helped shape British new wave and the New Romantic movement, but also how they seem ready for hits again.

It’s gutsy to put so many new songs in a set for a crowd that hasn’t seen you in 32 years or heard from you in 29. But Spandau Ballet, despite the waistcoats and the balladeering, were always ready to fight (and not just internally).

“When we got back together five years ago, we came up with this song,” guitarist Gary Kemp said, introducing, “Once More.” “It sort of summed up our situation.”

Recorded as more of an acoustic ballad, “Once More” picks up some grit and power in concert, especially as singer Tony Hadley puts some punch into the line, “Let’s rise up together and take on the world.”

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Even the stylish adult pop single “Steal,” which came out of the band’s sessions with producer Trevor Horn, gets a bit tougher. “It’s so nice getting played on American radio after all this time,” Hadley said following “Steal.” (BTW Nashville, “Steal” would be a country smash if some bro would strip it down and twang it up.)

The band’s reinvention doesn’t stop there. The focus on its early, avant-garde electronic roots works well, especially when saxophonist Steve Norman picks up the guitar to beef up “Confused” and “The Freeze,” so that bassist Martin Kemp and drummer John Keeble can go all out on the pounding rhythm. And Hadley’s ever-booming voice, seemingly even stronger now than it was in his younger days, soared above it all.

However, it was Gary Kemp’s guitar playing that delivered the night’s biggest surprises. He has long added unexpected guitar touches to the band’s music – those funk guitar flourishes at the end of “True” are only the beginning – but there were some doozies Saturday night. In the ballad “I’ll Fly for You,” following a fiery sax solo from Norman, Gary Kemp delivered a searing guitar solo that would fit into a Prince set circa “Purple Rain.” He added a bit of ZZ Top-ish Texas boogie to the end of the synth-driven “Communication.” And he punctuated the uptown funk of “Chant No. 1 (I Don’t Need This Pressure On)” with a great groove and a bit of a rap.

Of course, there was some nostalgia. The songs from their classic “True” album were massive sing-alongs – which even helped Hadley a bit when he got lost in the first verse of “Lifeline” – and the band was all smiles and hugs after a powerful version of “Gold” as the crowd roared for more.

“We didn’t know what to expect,” Hadley said. “But we didn’t expect this. Thank you.”

SETLIST: Soul Boy / Highly Strung / Only When You Leave / How Many Lies? / Round and Round / This Is the Love / Steal / Chant No. 1 (I Don’t Need This Pressure On) / Reformation / Mandolin / Confused / The Freeze / To Cut a Long Story Short / Raw / Glow / Empty Spaces / Gold (acoustic) / Once More / I’ll Fly For You / Instinction / Communication / Lifeline / True // ENCORES: Through the Barricades / Gold