“I don’t believe we’ve played this bar before,” Jack White, leader of garage blues revivalists the White Stripes, cheekily told a swaying sea of 18,000 devotees at Madison Square Garden on Tuesday night.

It’s not that Mr. White and his ex-wife and drummer, Meg White, haven’t been around the block — after 10 years of touring and six studio albums under their candy-coated belts, the twosome’s minimalist brand of power chords, roadhouse melodies, and school yard sing-alongs has led them around the world. But with the ink still drying on their major-label contract and their first arena tour still in its infancy, one got the feeling that the fans at the Garden were hosting the Stripes as much as the Stripes were hosting them.

The Detroit duo began a decade ago as little more than an experiment in fuzzy austerity and a novelty of peppermint aesthetics before growing gradually — rather than overnight, thankfully — into a blues-rock behemoth. With just Mr. White’s guitar (and occasional keyboard) and Ms. White’s drums to propel the sound waves, it has always been crucial for the Stripes to command their rooms like the blues preachers and tent revivalists after which they pattern themselves. Early in their career, when they lived on the fringes of the rock scene, that command came easily in smaller rooms; Mr. White’s guitar would lash out erratically like a downed electrical wire, his voice crackling through the amplifiers, and Ms. White’s infamous rhythmic simplicity — maligned by some on record — would benefit the mix by anchoring, rather than having to embellish, the songs.

By contrast, the booming echoes of the Garden can make an act, even one with a sound as big as the White Stripes’, seem very small. But such is life for a top-flight, million-selling rock ‘n’ roll band; now that the mainstream is at their doorstep, can the Whites evolve one more time into a victorious arena act?

If their first Garden party is any indication, the answer is … they’re working on it. Precision, at least in concert, has never been the White Stripes’ hallmark, nor has it been their ambition. In the studio, multiple tracks and supplementary instruments have allowed Mr. White’s limitless creativity to roam free, and have also taken much of the burden off Ms. White to keep the ship from veering off course. In concert, Mr. White’s volatile guitar playing places that burden more squarely on her shoulders. For a drummer as rudimentary as Ms. White, contrast is everything; her discreet segues from the high-hat to the crash, or from the tom to the snare, steer the group’s songs from section to section and prove that you don’t need to be a technician to understand dynamics.

On Tuesday night, it was difficult to distinguish these contrasts. Multi-section numbers such as the brooding “I Just Don’t Know What To Do With Myself” and the slide dirge “Death Letter” — though both electrifying, as always, in a way only the White Stripes can be — nearly drowned under the weight of the sound bouncing back to the stage from the arena’s concrete walls. Without Ms. White’s crisp cymbals to call out the changes, her ex-husband’s guitar was sometimes left lacking its own sense of direction.

Still, though his fingers may wander from time to time, and though his pick may stub a string rather than stroke it every now again, Mr. White is nonetheless a champion of rock guitar and a master showman. He’s John Lee Hooker rather than B.B. King — raw, unrestrained, impulsive — everything rock is supposed to be but rarely is for $50 a ticket. From the warbling, descending chords of set opener “Dead Leaves and the Dirty Ground” through the Southern stomp of “Icky Thump” and the staccato power strum of “You Don’t Know What Love Is (You Just Do As You’re Told),” Mr. White never let his audience squirm free from his grip, stabbing and strangling his big Eastwood guitar like a tornado with a red T-shirt.

Tellingly, though, the evening’s two most reserved songs did the most to connect the White Stripes to their expanded minions. The duo never plays from a set list, and usually relies on visual and sonic cues to stay together. So when Mr. White began picking the chords to the febrile, Peggy Lee-inspired “In the Cold, Cold Night” — one of Ms. White’s rare lead vocals for the group — the look of surprise and sudden nervousness on the drummer’s face was unmistakable. As she sauntered to the center-stage microphone to anticipative applause, she closed her eyes and began to sing, as would a 9-year-old practicing for the school play in front of her parents. It was as charming a moment as you’re likely to see at a rock show.

About an hour later, as the duo rolled through a six-song encore, Mr. White slung his acoustic guitar over his shoulder and played an oldie but goodie, the school yard ballad “We’re Going To Be Friends.” The sweet and simple chords were a contrast to the heavy lifting he had done much of the night, but it was the lyrics, so intimate in such a cavernous room, that seemed to reach forward into the mass and bridge the chasm between two performers and 18,000 paying customers.

“Tonight I’ll dream / while in my bed / when silly thoughts go through my head / about the bugs and alphabet / and when I wake tomorrow I bet / that you and I will walk together again / I can tell that we are going to be friends.”