On Saturday lunchtime, as half of New York quaffed their Eggs Benedict at brunch, Björk was inside Carnegie Hall spilling her guts.

The matinee concert (the first of a string across the city during the next month) began at just after noon and reached an early peak with the song “Black Lake.”

Taken from her ninth album “Vulnicura” – a gripping elegy to her long-term relationship with artist Matthew Barney – the track was recreated with so much naked emotion and power, it was a wonder that the Icelandic singer managed to keep herself together for the entire ten-minute duration.

The song flitted between string-laden moments of sorrowful reflection to heaving, beat-tracked fury.

“Family was always our sacred mutual mission/Which you abandoned,” goes one especially cutting line, which felt like a dagger in the ear for even the most neutral of parties.

Heartbreak is bread-and-butter for most pop singers, but the agonizingly visceral way in which the 49-year-old often articulates it makes Sam Smith sound like a bed-wetting adolescent in comparison.

In contrast to the high-concept, technology-heavy bent of recent tours, Björk’s latest stage set up is minimal. A 15-piece orchestra and some low-key projections provided her backdrop and even Björk’s nest-of-needles headpiece was ditched at the intermission.

But the hefty subject matter for the songs on “Vulnicura” meant that there was still plenty to command attention.

The first half of the set featured the first six songs of the album, sung meticulously by Björk’s wavering voice which, remarkably, doesn’t seem to have changed since she began fronting Icelandic indie-rockers the Sugarcubes in the mid-1980s.

The second half saw Björk dipping her toe into the past, but not to pull out the hits.

Songs such as “Come To Me” (from her 1993 album “Debut” and by far the oldest played), as well as a serene version of “Undo” were seemingly pulled from the archives to add to the show’s theme of love and devotion.

Especially poignant was the makeover of 2007’s “I See Who You Are,” in which she beautifully describes a metaphysical bond that will last until death. Björk must look back to it in hindsight and wonder if she was actually blind all along.

But like the album, a much-needed resolution came to the show in the shape of the sturdier, more electronic closing songs.

“Quicksand” ramped up the energy in the auditorium thanks to an attack of swirling rhythms and finally, “Mouth Mantra” saw Björk singing of breaking vicious habits and doing things she hasn’t done before.

To underline her spiritual rebirth, she took to the edge of the stage and proudly delivered the line “I am not hurt” to a swell of pointed applause.

It wasn’t easy listening, but watching and hearing how she picked up the pieces of her life makes Björk’s return to the stage feel all the more triumphant.