Tori Amos put her songs first on Sunday night. Literally. Welcoming a capacity crowd to the third of three sold-out shows at the Theatre at Ace Hotel, the veteran singer and pianist said it had been a privilege for the songs — “and for me” — to be heard by audiences across North America over the last few weeks. Sunday’s show concluded a tour behind Amos’ recent “Native Invader” album, and like the other gigs, it was emphasizing music over the type of spectacle and pageantry that pop concerts are often built around. Seated between a grand piano and a rack of keyboards, unaccompanied by a band, Amos sang and played with vivid determination as she moved through complicated, deep-feeling tunes from her extensive catalog: “Pretty Good Year,” about a young person struggling with apathy; “Russia,” a politically inspired song from the new record; “Alamo,” which she cleverly intertwined with lines from Sade’s “Smooth Operator.” During “Juarez,” she used the fallboard over the piano’s keys to smack the body of the instrument for a startling percussive effect — just one example of her commitment to her raw materials. To some degree, Amos was eschewing the pop-star stuff, because these days, she’s not much of a pop star. “Native Invader,” with songs about nature and family and the uncertainties concerning government embodied by President Trump, is the singer’s 15th solo studio disc; it comes long after Amos, who’s 54, stopped creating radio hits (such as “God” and “Cornflake Girl”) and began playing to an ultra-loyal core eager to hear her follow her every artistic impulse. Lately, those have included theatrical works and forays into classical music. Yet “Native Invader” marks a return in a sense to the florid but earthy voice-and-piano sound of early records like “Little Earthquakes” and “Under the Pink.” The album’s opening track, “Reindeer King,” which Amos performed at the Ace, has the kind of swooping vocal melody and cascading piano part that made her a name brand in the early 1990s. In Taylor Swift’s 2017, though, that style hardly represents a mass-market proposition — unless, of course, it arrives in the hands of someone much younger, such as Adele or Sam Smith.