Five tracks into Annie Clark's fifth album as St Vincent comes a song called Digital Witness. "If I can't show it, you can't see me," she sings, over a distorted 80s R&B backing, lent a hint of unease by the oddly dense, claustrophobic horn arrangement. "What's the point of doing anything?" It's a satire on the Facebook generation's need to document and display their lives, a digital update of Ray Davies's old suggestion that people take pictures of each other just to prove that they really existed. But it could also describe this album's promotional campaign, in which Clark has popped up pretty much everywhere, doing pretty much everything. She's appeared at a fashion show celebrating the 40th anniversary of Diane Von Furstenburg's wrap dress, at which she sang, modelled a version of said dress and told the assembled press that her style icon was Albert Einstein, which at least goes some way towards explaining her recent radical transformation in the hair department. She's tried her hand at comedy, reading out a one-star Amazon review of the Beatles' Sgt Pepper on a US TV show. Meanwhile, over on teen website Rookie, Clark has been both demonstrating her soccer skills and dispensing big-sisterly advice to her young audience: "You can master things with enough time and effort." She's yet to fetch up on Benefit Street, conversing over a can of Kestrel Super with Fungi and White Dee, but, in fairness, there's still an episode left.

It all underlines the image of Clarke as a polymath: a woman credited with playing 13 different instruments on her 2007 debut Marry Me; who comes from solid US indie-rock stock – a former collaborator with Sufjan Stevens and the Polyphonic Spree – yet plays guitar in a way that's attracted attention from the kind of music magazines that don't usually have a lot of space for fine-boned, Pitchfork-approved, female art-rockers. Amid the reviews of the Pigtronix War Hog Ultra High Gain Metal Distortion Pedal and the features drooling over Slayer's guitars ("the most well-known axe is a Schecter signature Damnation model with a 'blood splatter' finish"), one such title recently found time to praise Clark for both her "sludge-fuzz blasts" and her "fancy-ass Steve Howe runs".

Indeed, if you wanted to level a criticism at Clark's early albums, you might suggest that she was perhaps too much of a polymath for her own good. There were some great songs, and she had a fantastic voice, but Clark was audibly a graduate of the same more-is-more school as her former collaborators. Those fancy-ass Steve Howe runs had to fight for space with horns, choirs, baroque strings, woodwind: it sometimes felt surprising that the list of 13 different instruments she played didn't include the kitchen sink. There's a sense that her solo career hasn't been about progression so much as refinement. By the time of 2011's Strange Mercy she'd succeeded in marshalling her surfeit of ideas into something approaching a skewed and hugely appealing take on pop, with the tension between the airiness of her vocals and the corrosive impact of her guitar playing at its centre. This album pulls things into sharper focus still.

The music here feels taut and meticulous, devoid of self-indulgence. There is indeed some impressively dexterous and angular guitar playing on Birth in Reverse – as people who drool over Slayer's axes might put it, Clark really shreds – but you scarcely notice it on the first few listens. It arrives in a couple of short bursts at the end of the song, less immediately ear-grabbing than the chorus, or the nagging glam riff that drives the verses, or indeed the lyrics: "Another ordinary day, take out the garbage, masturbate."

Relegating your own own guitar heroics to a tiny cameo role is a mark either of humility or confidence. In fact, the most striking thing about St Vincent is how confident it seems: from its title to the opening crunch of distorted drum machine to the gorgeous closing ballad, Severed Crossed Fingers, it feels remarkably sure-footed, the sound of an artist who, when not taking out the garbage or masturbating, has worked out exactly what she wants to do, and furthermore exactly how to do it. It's tempting to wonder how much her confidence has to do with her 2012 collaboration with David Byrne, Love This Giant, a faintly underwhelming album that nevertheless seemed to confirm Clark's ascendancy to greatness: it clearly wasn't intended as a kind of pan-generational art-rock face-off (you can hear Byrne's influence on the jerky funk and nervous outsider protagonist of St Vincent's first track, Rattlesnake) but ended up feeling like one, simply because most of its great moments seemed to emerge from Clark rather than the old master of smart-alec rock. More likely it's down to the fact that Clark has written the strongest material of her career.

St Vincent's 40 minutes offer an embarrassment of fantastic songs: the electronic judder of Psychopath, the sumptuousness of I Prefer Your Love. It feels emotionally lighter than its predecessor – last time around there was a lot of sex, some of it a bit painful in every sense, whereas this time there's a lot more love – but Clark still comes up with some startling lyrics. Floating along on a kind of synthesised spectral chorus and blessed with the kind of tune you just want to wallow in, Prince Johnny is a fascinating puzzle: it's hard to work out whether the titular character is male or female, whether or not the song's narrator has slept with him or her, or how much their affection is tinged with contempt. In fact, the words are often ambiguous – Digital Witness isn't the only song about the disparity between public image and reality – but they're the only thing here that is: bold, poised, precise without sounding sterile, St Vincent seems to be a straightforward triumph.