Sting and Peter Gabriel get cozy with each other’s material at the Hollywood Bowl

Peter Gabriel had a stark realization before hitting the road with old pal Sting for their joint Rock Paper Scissors tour: He was going to have to stand next to the famously fit former Police-man.

So, the more generously proportioned ex-Genesis frontman decided to hit the yoga mat. Gabriel told a Hollywood Bowl crowd Sunday that he didn’t see results at first, until Sting helpfully noted that he would actually need to move on said mat.

On Sunday night during the first of the Brit rock pair’s two sold-out shows, Gabriel quipped that after a mere three lessons, “No one backstage can tell us apart. We’re known as the Tantric twins.�

The Rock and Roll Hall of Fame-ensconced duo — backed by the combined power of a baker’s dozen of world-class musicians — played two hours and 40 minutes of some of their best-loved songs with a giddiness and verve that illustrated the enduring nature of their catalogs. From “Solsbury Hill� to “Sledgehammer� and “Message in a Bottle� to “Desert Rose,� and many points in between, the show was a gleeful jukebox of impeccably played songs.

Affectionately spurring each other on all evening — Gabriel kept referring, with endearing goofiness, to his comrade as “Mr. Sting� — the pair traded vocals, sometimes took lead on each other’s songs, provided backup and danced side by side in a performance that ran the spectrum from sobering politically conscious ballads to ecstatic full-tilt rockers.

If Gabriel is perceived as the more solemn of the pair — with his patented still-to-explosive tunes, such as the frenetically percussive opener “The Rhythm of the Heat,� which moved from claustrophobic to manic — he was also the most active and verbose. He busted out his patented bounce and spin dance moves and waxed comic about a previous visit to Los Angeles in which he was approached by a man at a party who offered his help. The man was a plastic surgeon.

Sting was quieter and more rooted to his bass but just as nimble vocally, reaching back for the high notes of the ’70s and ’80s with impressive effortlessness.

Occasionally, one would cede the stage to the other. Sting’s band ripped through Police classics “Every Little Thing She Does Is Magic� and “Roxanne.� Gabriel, meanwhile, lit into “Big Time� and moved with the gospel-inflected duet “Don’t Give Up,� accentuated here with gifted backing vocalist Jennie Abrahamson. He also took a near solo turn on the poignant “Love Can Heal,� dedicated to the late British MP and friend Jo Cox.

The mention of Cox’s shooting death was one of several nods to the state of current global affairs. While flags flanked the stage at half-staff, the two segued from the Police’s percolating lament “Driven to Tears� into Sting’s meditative “Fragile,� which he prefaced with a speech about combating unspeakable cruelty and mindless hatred with empathy. Next was Gabriel’s propulsive cri de coeur “Red Rain,� resulting in a powerful one-two-three punch. Sting also nodded to Brexit by singing a bit of Genesis’ “Dancing With the Moonlit Knight.�

The night was more uplifting, however, when both men were onstage reinterpreting each other’s songs or singing in harmony. Sting took the lead on Gabriel’s hip-shaker “Shock the Monkey,� Gabriel gave Sting’s “If You Love Somebody Set Them Free� a casual bluesy and serpentine retrofit, and they joined for a triumphant take of Gabriel’s “In Your Eyes� that found Sting and Abrahamson subbing for Youssou N’ Dour.

�Every Breath You Take� and “Sledgehammer� put a joyous exclamation point on what was a lively musical conversation.

Near the start, Sting had said that the shows had prodded both men out of their comfort zones. Perhaps, but they clearly found common ground.

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