"Usually by this point I'm throwing up and apologising to everyone for what they've just watched," Perfect Pussy frontwoman Meredith Graves confesses, in atypically self-assured mood, once the last drones of her band's set have faded barely 30-minutes after it began. Then she adds: "You guys are great, everyone is great."

Don't be fooled by their jailyard tattoos, the fireball attack of their playing or their Google-baiting name. This New York fivesome – whose debut album Say Yes to Love arrived via Brooklyn's excellent Captured Tracks – are the self-styled "nicest fucking band in punk". They're the hardcore kids you can hug, led by the Courtney you can love.

Bleached-blonde hair clipped short, a red jumper tied around her waist, Graves leaves no square inch of the air around her violently unmolested during Perfect Pussy's two-minute sonic maelstroms. Bassist Greg Ambler and guitarist Ray McAndrew – whose Joanna Gruesome T-shirt pays tribute to tonight's support – are similar blurs of inky flesh. Keys player Shaun Sutkus contrastingly stands stock still as he conjures electronic hisses and whirrs.

As one number collides into the next, even hardcore fans might be hard pressed to differentiate I from III (several songs are titled after Roman numerals). Lacking confidence in her voice, Graves' vocals are indecipherably buried deep in the mix. But this is music that is much less about detail than the aggregate sense of raging righteousness it sends coursing through guts and ears.

It would be nice to be able to discern just some of Graves' lyrics, though: her body-language – veins in neck bulging as she howls – implies she's singing things more meaningful than, say, her shopping list. Like the unnecessarily angsty chat at the end, it's something to be outgrown if Perfect Pussy are to make a lasting statement. But for now, we can be content admiring a group in rare control of punk rock's fabled raw power.

• At Visions festival, 2 Aug, London.