Marilyn Maye takes a stage like Grant took Richmond, MacArthur returned to the Philippines, or Sherman marched through Georgia. The great cabaret singer doesn’t just reach out to an audience — she overwhelms it with a song, but in the hippest, most swinging way imaginable.

On Tuesday night at Rose Hall, for the second evening of the Mabel Mercer Foundation Cabaret Convention, Ms. Maye began with “The Song Is You” in an orchestration (which she’s been singing for at least 35 years) that’s so exciting as to be almost confusing when described on the page: It’s a big, belting, modulating, polyrhythmic, multitempo, song-quoting (“I Hear Music”), over-the-top treatment — and if that isn’t enough, it even goes into a 6/8 Afro-Cuban beat at one point (à la Nelson Riddle’s famous arrangement of “Come Rain or Come Shine”). Then, instead of cooling down, for her second song she built even higher, with a riveting treatment of a classic 1960s anthem of self-affirmation, “You’re Gonna Hear From Me.”

But just when we think Ms. Maye has to lower the electricity and the excitement level at least a notch, if only to give us a breather, she begins with Sondheim’s comparatively contemplative “Old Friends,” which turns out to be only the intro for her biggest rabble-rouser of all: Peggy Lee’s “Love Being Here With You,” which she sings with a sheer, raw energy that’s completely inapposite to the songwriter’s own performing style. Yet it works just the same.

Just a few years ago, Ms. Maye, 78, was so obscure that only the most diehard buffs of female vocalists remembered her (and barely, at that), even though she had made at least five excellent albums for RCA (released in the mid-’60s, precisely the wrong time for a singer of traditional standards to try establishing a career) and had made nearly 80 appearances on “The Tonight Show,” under the aegis of both Steve Allen and Johnny Carson. Then, last fall, she re-emerged in New York (first at the 2006 Cabaret Convention) and began appearing regularly at the Metropolitan.

Tuesday night’s set launched her third long run (a 10-show series that continues through November 19) at Rose Hall in 2007. Within the last few months, Ms. Maye has become a must-see singer in New York, so much so that wherever she sings, whenever she reaches the line, “I love to hear you call my name” (in “Love Being Here With You”), the crowd automatically yells out, “Marilyn!”

In the extra-musical aspects of her show, Ms. Maye unselfconsciously offers a time-capsule example of big nightclub (Las Vegas-style headliner shtick of 50 years ago) bits, such as kicking her heels high in the air on the appropriate line in “It’s Today.” Considering all these factors, one might be tempted to dismiss Ms. Maye as merely a surface-deep belter. But she doesn’t just holler the words — she knows how to make you feel them. When she sings “You’re Gonna Hear From Me,” she makes it sound like a personal manifesto custom-composed for her by André and Dory Previn.

Equally important, Ms. Maye’s rhythmic chops are every bit the equal of her lung power: She swings on everything she does, and uses the force of the beat to drive home the meaning of the text. Even on “Take Five” (she was supposedly the first to sing Lola Brubeck’s words to Paul Desmond’s jazz classic, on her CD “Sounds of Maye”) she unleashes a complicated libretto on a fast 5/4 tempo, and sounds even more comfortable scatting the thing. “Rain” tells the tale of Somerset Maugham’s femme fatale, Sadie Thompson, in an out-and-out mambo tempo. “Golden Rainbow,” on the CD, is another, possibly even more exciting, hybrid of Broadway, swing, and Latin styles.

Ms. Maye may be all Vegas-Copacabana-style showbiz, but her background is Kansas City swing — she was raised during the famous Pendergrast era of Count Basie and Lester Young, and it obviously ignited her capacity for rhythm as well as her affinity for the blues. Her most poignant numbers are associated with the black American tradition, such as Arlen & Mercer’s blues-inflected “Come Rain or Come Shine” and Lil Armstrong’s remorseful “Just for a Thrill.” Her latest album is “Maye Sings Ray,” and Ms. Maye is virtually the only singer I’ve ever heard in the history of the Cabaret Convention whom I would want to hear on a tribute to Ray Charles.

On Tuesday, in the middle of her tribute lyrics to the late Brother Ray on “Hallelujah! I Love Him So,” Ms. Maye told us, “I’d like to sing like him, but I’m too white.” No such apology is necessary. Unlike Ray, however, Ms. Maye focuses on the exuberant, up-tempo side of the blues; she never sings the sad, slow blues. Pete Hamill once famously said that Frank Sinatra’s swing numbers existed mainly in relief to his downer ballads, and with Ms. Maye, it’s precisely the opposite: She only occasionally slows the tempo slightly as a respite from all the killer fast numbers. Although a few ballads appear on her vintage ’60s albums, Ms. Maye avoids truly slow, intimate love songs that require her to show vulnerability.

Even if you have to look elsewhere for intimate ballads, taken altogether, Marilyn Maye is a helluva package; her show is all dramatic entrances, climaxes and big closers with no filler.

wfriedwald@nysun.com