Why would you ever perform Beethoven 1 and 2 today? Beethoven wrote seven later symphonies which are clearly better. That's kind of the point of Beethoven. Looking back on these two quite early works given knowledge of those masterful symphonies yet to come, it's hard to justify their performance except as stages in a story – a story which, if truth be told, is pretty familiar.

But if told well, the story of Beethoven's symphonies can still be completely compelling – and Daniel Barenboim is a storyteller of the highest quality. His Beethoven symphony cycle at the Proms kicked off on Friday night with performances of Beethoven's first two symphonies – sandwiching some impeccable, gorgeous Boulez – which fully justified yet another retelling of the Beethoven legend.

The affinity between Barenboim and his West-Eastern Divan Orchestra was clear immediately, Barenboim often needing only the lightest of touches to elicit a tight, precisely phrased response from the players. The First Symphony was particularly beautiful in its execution, classically delicate like Mozart but with moments of richness in tone and expansiveness in phrasing which hinted at the Beethoven of the future. Especially striking, the second movement saw Barenboim embarking on a series of long, fluid, eminently Romantic journeys, only to jolt out of them with moments, like the recurring triplet figuration, which come straight from the 18th century: this is Beethoven on the edge of something bigger, but only sometimes. The third movement as well, all filigree twiddles and sudden crescendos, only hinted at the manic Beethoven scherzos yet to come – though hint it did, at a ruthlessly fast pace and with no room for pause between the sections.

Closing the concert, no. 2 was somehow not quite as electrifying as no. 1; Barenboim perhaps took this work a little more as an orchestral showpiece, with the strings shining in particular in the first movement. But while the players certainly sounded superb, there was just a touch less insight in this rendition. The second movement, somewhat bigger than that of the First Symphony, was played in a noticeably more Romantic style, but for all the beauty of the orchestra's tone the thread seemed lost at times. And while the third movement of no. 1 was excitingly fast, that of no. 2 felt a lick too much so – as did the finale, although the pacing of this movement was magnificent, unfolding like a single sentence, and with the most convincing of conclusions. Despite a few nitpicks, then, this was still Beethoven in the hands of an authority, played with dazzling style and wit.

Barenboim's authority was equally indubitable in the concert's middle piece, Pierre Boulez's Dérive 2 for 11 instrumentalists. Each pair of Beethoven symphonies in this cycle is being complemented by some Boulez in between, and while this seems peculiar on paper (and almost a parody of the perpetual habit of concert programmers to "sandwich" contemporary works between canonic ones), something about it worked well. Barenboim naturally seemed rather stricter here than in the Beethoven, unsurprising given the increased demands of the score, but I absolutely got the sense that he was approaching this piece in the same way. The fluidity, the drive, the sense of drama: these were all still here in spades.

Of course, the music sounded rather different from the Beethoven, bubbling along insistently, full of bright, cartoonish colours and ebb and flow. It's an intense listen but also hugely communicative, which counterpoints its sense of freedom or drift ("dérive") to the sort of logic in development expected of Boulez. There is humour in it, for all its rigour; it's like a Wacky Races cartoon penned by Samuel Beckett, possibly. And the players sounded excellent: they found a well-balanced sound within the hall's acoustic, and played the piece – as they did the Beethoven – with brilliant pacing.

There's no doubting that the concept of this Beethoven/Boulez cycle is a bit weird, but this opening concert's excellence in performance swept my concerns away. You can argue that Boulez stands at the end of a line which Beethoven and his symphonies set in motion, and familiar though the story is, it's clearly good for another telling or two. Stories are only as boring as the storyteller makes them, after all, and Daniel Barenboim has certainly caught my attention. This is the only one of the cycle that I'll be reviewing, but I'll certainly be back for more. It's unmissable stuff for fans of Beethoven, Boulez, or music.