Prom 45: The Makropulos Affair, BBCSO, Bělohlávek

Karel Čapek, the great Czech writer who pioneered some of the most prophetic dramatic fantasies of the early 20th century, thought Janáček was nuts to want to set his wordy play about a 337-year-old woman to music. He could not have anticipated what that septuagenarian genius would achieve. Some of us felt similarly doubtful about singers performing this most conversational of operas with scores and music stands in a "concert staging".

But the Albert Hall can be as surprising and as unpredictable as Janáček, and it helped a dream cast, conductor and orchestra to produce vintage Proms magic.

This, in short, was the most electrifying Proms opera since Nina Stemme and Donald Runnicles pulled it off in Strauss’s Salome, and so many things that the concert Jenůfa at the Festival Hall in April, for all its sonic beauties, was not. Karita Mattila (pictured below in Act One), glued to the score on that occasion in preparation for a role she had yet to sing on stage, knows the part of the 1920s diva Emilia Marty, born Elina Makropulos in 1585, inside out. With her ageless beauty and that unique incandescent sound, Mattila can embody the strangeness of a woman whose soul has died within her and yet who still longs for release.

Physically, the gestures are writ perhaps larger, in the first act at least, than they would be in the realistic production setting of a lawyer's office, but how clearly she made her reactions felt for those in the audience who hadn't bought a programme, didn't know the opera and had to do without supertitles (still a great drawback of the Proms – surely they could fill the hall with enough screens to make it work?) The comedy got the laughs on cue, not least when Marty declares that a long-dead rival diva "squeaked" ("Strada piskala"). Had she been studying flamenco arm movements for the intermezzo with the decayed suitor who recognises in her the gypsy "Eugenia Montez" of a previous existence?

As for the great final scene (pictured below), where the diva tells the assembled company how lucky they are to have a natural life span where everything still has meaning, Mattila kept it simple, allowing the voice to pour forth an emotional stream of Janáček's unique bel canto. Plenty before this was beautiful to listen to; the role may have had great singing-actresses to thrill on stage, above all the inimitable Anja Silja at Glyndebourne, but it has surely never sounded so lovely as well as expressive.

The same could be said for a BBC Symphony Orchestra on simply amazing form under Jiří Bělohlávek, who knows the Janáček scores probably better than any other living conductor. If his Jenůfa with the Czech Philharmonic projected warmth but not bite, the typical sound of a Bohemian ensemble rather than one from Janáček's native Moravia, this – like the playing of the ENO Orchestra under Mark Wigglesworth in a near-perfect Jenůfa – captured both, and specifically the fire and ice of a more singularly orchestrated score, projecting into the hall the inspired ideas, enough for 10 operas, which drive the music forwards for a minute or two each and then are gone.

Seconds into the longest of the composer's operatic preludes, pittting passion against the fanfares of the past – as in Wagner's Lohengrin, the composer doesn’t reveal what the other-worldly music means until the Act Three denouement – we were hearing unbelievable sounds from piccolo and first horn, ostinato figures usually smothered by the strings. The clarinet family, too, worked wonders of warming colour, and Bělohlávek's pacing was a miracle – letting sympathy surface through the legal wranglings early in the action through a held chord, a dramatic silence, working the spaces of a hall he knows well not just as a conductor but also as an Arena Prommer.

All the singers delivering idiomatic Czech were simply perfect, as the supporting cast had been in the concert Jenůfa. Four tenors, older and younger, reminded us how Janáček's homeland still produces a special type of high voice type. Aleš Briscein (pictured below) as Albert Gregor went for the top notes fearlessly and conveyed all the bewilderment of the non-love scenes with the woman who turns out to be his grandmother (or great-great-great-great-grandmother, as Marty later claims). It sounds as if Aleš Voráček, as the hapless Janek bewitched by Marty and bullied by his nasty father Baron Prus (Svatopluk Sem, as vivid in dark-hued projection as Gustáv Beláček's lawyer Kolenatý), also has a future in major roles. Eva Štěrbová as Janek's girlfriend Krista, the young singer infatuated with the diva's example, characterised beautifully – spirited and debutantish like The Sound of Music's Liesl in Act One, conveying numb misery and then acceptance simply by her body language towards the end as Marty's fate becomes clear.

Never underestimate the role of a director in a concert performance like this. Kenneth Richardson and his (uncredited) design team did a fine job. Costumes were right, as the evening dress had palpably not been in the Festival Hall Jenůfa, and for once the back display, which reached an apogee of hideousness at the start of Wednesday night's Prom with mint-green toothpaste swirls against black for Barenboim and the West-Eastern Divan Orchestra, had meaningful and well formed images. I liked the brief appearances of the telephone, the old portrait of Mattila when the question of a signed photograph arises, the booze for Marty's drunken revelations (just a pity that this last detail didn't yield to a portrait of Rudolf II when Marty narrates the history of the life elixir).

We also got green, as the stage directions indicate, at the start of the most exultant of operatic endgames, yielding to a magnesium flare as the elixir's prescription finally goes up in flames.This of all Proms should have been televised; we could have watched it again and again with subtitles to boot. As it is, the visuals, above all Mattila's diverse poses, will live on in the minds of those who saw them, while the astonishing sounds can continue to resonate, for a while at least, on iPlayer.

• Listen to this Prom for the next month on the BBC iPlayer
• Read more Proms reviews on theartsdesk