Walking in to this most iconic of music venues, under a full harvest moon, concert-goers were greeted by a digital billboard of Tom Petty and the stark message, “1950-2017.” So it was a pleasant surprise, settling in, to hear The War on Drugs’ frontman/guitar hero Adam Granduciel stray from the set’s usual opener to launch, unannounced, into a plaintive version of Petty’s “Time to Move On,” a track from his 1994 solo album, “Wildflowers,” its opening verse sadly appropriate, “It’s time to move on, time to get going/What lies ahead I have no way of knowing/But under my feet, baby, grass is growing.”

Just three-and-a-half years from headlining the Troubadour, then graduating to the Greek in October, 2015, The War on Drugs return with its major label debut, “A Deeper Understanding,” on Atlantic Records, its fourth full-length since the 2008 indie bow, “Wagonwheel Blues.”  Now a six-piece, led by Granduciel — who looks more like a lumberjack than a rock star with his red-plaid man-tailored shirt, lanky dark hair and beard — the band is positioned to inherit the title of best American arena classic-rock band from Petty and the Heartbreakers, who completed their acclaimed, victory-lap 40th anniversary tour just a week before its leader’s untimely passing.

Granduciel is an unassuming focal point, and this 16-song, two-encore set reflected its recent album title, offering a deceptively slow-burn approach that juxtaposed his own conflicting, often self-masochistic desires. While seemingly willing to submit to the captivity of desire (on “In Chains,” he sings, “I’m in chains/I’m in love/I’m in pain”), he often juggles rapture and heartache (in “Strangest Thing,” he asks, “Am I just living in the space between/the beauty and the pain?” amidst Robbie Bennett’s cascading stream of synths and keyboard fills).

The tremolo-bar-bending on the aptly named “Pain” channels Petty’s guitarist Mike Campbell, while the epic scope of the Dylan-meets-Roxy Music “An Ocean In Between the Waves” balances Granduciel’s high-pitched, mellifluous solos with the bottom-heavy bleat of Jon Natchez’s buzzing baritone sax. All told, TWOD perform nine of the 10 songs from “A Deeper Understanding,” with the propulsive guitar solo on “Nothing to Find” about a third of the way through finally bringing the crowd to its feet, where they remained through the soulful R&B of “Knocked Down” into the signature soundscape of “Lost in the Dream,” with an aching Granduciel harp solo underneath the glowing lunar orb seemingly reflecting Petty’s “Full Moon Fever” spirit.

Granduciel uses his guitar solos as spiritual escapes from the tyranny of his desires, with his New Jersey/Philly roots most apparent in “Eyes to the Wind,” with its nods to Jackson Browne, Elliot Murphy and fellow Garden State icon Bruce Springsteen in the extended guitar/sax interplay. There’s more pain in “Burning,” set against a swirling carnival organ and some spiky guitar feedback, the only nod to theatricality a pair of inverted parentheses in the form of an “X” with two rows of flashing lights as a backdrop.

Indeed, the War on Drugs are all about the music, specifically, the cool, fluid tones of Granduciel’s guitar, but the band itself – along with Bennett and Natchez, it includes bassist David Hartley, guitarist/keyboardist Anthony LaMarca and drummer Charlie Hall – provide the perfect cushion for instrumental forays, with Hall’s techno pulse giving this classic rock a modern edge.

By “Up All Night,” Granduciel even dropped his button-down approach for a few spirited “whoops,” as he wrangles his guitar to sound like a synthesizer with some pneumatic riffing that explores “the hole in my head” in an interlude that comes straight out of the Grateful Dead playbook.

The only quibble is, after a while, the guitar solos sort of blend in to one another, but that’s kind of the point, even as their reliance on tunefulness helps distinguish them. Still, the set-ending “Clean Living” proved a bit anti-climactic, serving as a way for Granduciel to introduce the other stage members, but the crowd brings them back for a rousing three-song encore.

“Brothers” is the oldest number the band plays – from 2011’s “Slave Ambient” — and “Red Eyes” remains arguably the group’s signature psychedelic anthem, while “In Reverse,” with its stately, majestic “Avalon”-like sheen (and Granduciel’s closing harp solo) nods to influences like Dylan, and of course, Petty once again.

“When we’re living in the moment/And losing our grasp,” sings Granduciel, “Making it last with the grand parade in our past.” The War on Drugs managed to do just that on a clear night populated with more than a few ghosts.