It's remarkable that the 39-year-old Kronos Quartet had never played at the Proms before this Tuesday evening, but they seemed set for making up on lost time, with a literally spectacular performance of a typically diverse range of works from around the world. The group have the amazing habit of treating all the music they play – whether it's a Sofia Gubaidulina quartet or a Syrian pop song – in exactly the same sincere, passionate manner. When the music is as stylistically and geographically diverse as in this programme, they hint at a beautiful, touching universalism – just as powerful, surely, as the much-discussed symbolism behind Daniel Barenboim's West-Eastern Divan Orchestra, who had been been performing earlier that evening.

Syrian musician Omar Souleyman's I'll Prevent the Hunters from Hunting You, as arranged by Jacob Garchik, became a vastly amplified duet for two violins over a plucked cello bass and percussion played by violist Hank Dutt. I honestly don't know how the quartet can pull off "world music" performances like this, complete with orientalised tunings, without sounding silly, but this proved a fantastic start to the concert.

A rather more serious middle section saw performances of the fourth quartets of both Russian composer Sofia Gubaidulina and the American Ben Johnston. The former, from 1993, is a beautifully delicate piece in which the live quartet plays against pre-recorded music for two more string quartets. Lighting effects – also used elsewhere during the concert – are specified as well. The players occasionally use a rubber ball, attached to a wire handle, which bounces softly on the strings, and the effect, here and everywhere in the piece, is quavering and mysterious, a wash of swishing, clustery tremolandos. Even the piece's intense climactic points are hushed. It's an extremely absorbing work, which demands meticulous, close attention, and – in a good way – it seemed to last far longer than the twelve minutes it apparently took.

Ben Johnston's 1973 piece, similarly pensive, is a set of variations on "Amazing Grace", which begins by taking this famous melody back to its Scottish roots but quickly moves into an eminently Kronos-esque realm of internationalism. Johnston uses various complicated tuning systems, but always with an eye (that is, an ear) to how they will sound, and he creates some beautiful sonic effects within the composition's fairly conventional variations structure. The song is always there; it even peeks out in cello harmonics during a passage which is otherwise all loud circuitous scurrying. Kronos' taste for eclecticism doesn't always give them the chance to fully demonstrate their virtuosity in the more traditional "Western" sense – but this quite conventionally complex work absolutely did, and they've very much still got it.

The evening's world première was a BBC commission by Canadian composer Nicole Lizée: The Golden Age of the Radiophonic Workshop (Fibre-Optic Flowers). It is a sort of tribute to the Radiophonic Workshop of the BBC, as mentioned in its title, and features (among various other electronic gadgets) a pair of tape machines which play a series of odd sounds, behind, in front of, and during the live quartet's performance. Lizée's programme note suggests a fascination with what she calls "The merging of the real with the unreal (on reel-to-reel)": the elements all combine to one big conglomerate noise. It's also dotted everywhere with surprises, such as the solo for "Simon" (a kids' electronic memory game) and the graceful, high violin solo which emerges from the depths to form a poignant ending.

The final piece was also the biggest: Serbian composer Aleksandra Vrebalov's ... hold me, neighbor, in this storm … is an emotional journey through Serbia's recent turbulent times which combines the quartet with the gusle, a traditional bowed instrument, as well as a harsh, military-style drum and the sound of church bells. It's wildly polystylistic, veering between almost cartoonish tonal passages and aggressive frenetic angst, with a sort of stunned lament following one of the angrier passages as well. It's very much a piece with a story to tell, which is what the Kronos Quartet do best.

There was a lot to enjoy in the concert, and of course by normal standards it was a ridiculously assured and inventive Proms debut – though I do have doubts about the programming, which was gloriously diverse but did threaten to lose cohesiveness as a result. The concert also provided evidence, once again, that music is better than lighting effects, and the parade of unsubtle colour changes added little aesthetically and occasionally got in the way a bit – even, in my view, in the Gubaidulina, despite being specified in the score. When the musical quality is as high as all this, a stage, some instruments and the Kronos Quartet is all you need.