Having celebrated his 85th birthday this past March, Bernard Haitink continues to demonstrate that he profits from the advantages of age whilst commanding the deftness of a conductor decades his junior. His programme at the Proms on Saturday evening with the London Symphony Orchestra offered musical perspectives on youthfulness and memory by way of Schubert and Mahler, culminating in the songs of innocence and experience of which the latter's Symphony no. 4 in G major is woven.

This year also marks the 60th year of the Dutch maestro’s professional life as a conductor, yet his podium demeanour exhibits not a trace of the ennui or arrogance of the supercilious elder statesman. The rapport between Haitink and the LSO musicians radiated mutual respect, collegial warmth, and – in the concert’s most memorable moments – a palpable sense of shared epiphany.

One of the benefits of Haitink's accumulated experience is his persuasive confidence with regard to proportion, whether in terms of the weight of a composition as a whole or the proper unfolding of its parts. Schubert wrote his Fifth Symphony before his worship of Beethoven had set in. Indeed, the teenage composer had yet to undergo his Beethovenian conversion; at the time he considered the older master an "eccentric" figure whose works were hampered by a confounding mélange of high and low. Schubert instead idolised Mozart as the purveyor, amid darkness, of "a bright, clear, lovely distance..."

Haitink understands the error of imputing inflated value to this sun-kissed score. The Fifth lacks the ambitious scope and reach of Schubert's later works. Yet the very lightness of this work, replete with smile-inducing charms, yielded some exquisite rewards in this account. For example, Haitink kept the Andante moving along rather briskly, refusing to linger until a moment of gentle sunset in the coda. The trio stood apart like a dreamy excursion from the sterner minuet enveloping it. In the outer movements, Haitink shaped antiphonal phrasings as more than local events but keys to the bigger picture. Without vulgar overemphasis, the players unobtrusively foregrounded the surprising harmonic modulations through which Schubert puts an individual stamp on Mozartean patterns.

The chamber-like scoring – Schubert omits clarinets, trumpets and timpani – posed an obvious challenge in the incongruously echoing acoustical setting of the Royal Albert Hall. Even so, the characterful playing of the LSO winds was beautifully etched and integrated with the ensemble's overall sound picture.

This particular care with sonic balance and colour turned out to be a focus of Haitink's Mahler 4 as well. (With this performance, he has now conducted the entire Mahler cycle except for Nos. 8 and 10 at the Proms.) As a Mahlerian, Haitink has a reputation for representing the "non-neurotic" end of the interpretative spectrum. The performance was grounded in a firm appreciation of the work's architectonic design and proportions, to be sure, but what stood out most was how the maestro elicited a sense of childlike wonder – or, rather, a sense of the adult's attempt to recover that lost wonder and innocence.

The first movement's oblique commentary on classical rhetoric – more Haydn than Mozart here – thus emerged as another metaphor for this attempt to recapture a lost, more "innocent" past. Haitink gave loving attention to Mahler's timbral combinations in the development as the primary signifier of this wonder, shaping an almost sculptural volume from the music's vertical configurations of widely spaced registers. Where another conductor might exaggerate such points for their own sake, Haitink's firm rein on tempo and momentum placed these in effective relief. This stoic, even "deadpan" approach was particularly refreshing in the Scherzo, ensuring an unusually sustained degree of clarity for its bizarre parade of sound colours.

So the slow movement also had a consistent, patient, inexorable flow punctuated rather than interrupted by each of its great climaxes (with the model of the Adagio of Beethoven's Ninth particularly evident in the background). I've encountered more visionary and moving interpretations of the immense serenity underlying the sorrowful outbursts of this music – Mahler once compared it to "the undifferentiated blue of the sky" – but Haitink doggedly refused to cater to mawkish sentimentality, giving it a curiously detached quality.

Repeating a fundamental gesture that is a hallmark of the Fourth, whereby Mahler simply brushes aside key moments of threat or apocalypse once these have been sounded, as if to start afresh, the final movement caps the work with a song and sets the Wunderhorn poem "The Heavenly Life", with its child's vision of heaven. Camilla Tilling was the captivating soprano soloist. Instead of opting for an unchangingly angelic "white voice", she gave a nuanced, multilayered interpretation that encompassed the movement's essential paradoxes, its conflation of innocence and violence, the celestial and the brazenly earthy.

For his part, Haitink took an essentially moderate approach: instead of exaggerating the contrasts of simple hymnlike cadences and the saucy, shrill outbursts that refer back to the music of the first movement, these were smoothed over. Whatever elements of nightmare intruded into the dream of bliss quickly passed by. The Proms audience waited through the coda's calming, fading repetitions and the return to silence before responding with prolonged ovations. Haitink came back onstage several times but at last closed the score on his podium stand, not wishing to disrupt Mahler's spell with an encore.