Prom 66, likely to have been Sir Simon Rattle’s last outing at the festival as chief of the Berliner Philharmoniker, managed that rare feat of thrillingly bringing to life a mostly well-worn programme of repertoire war horses. He and his orchestra did so in a performance which was exhilarating and revelatory at every turn, making a compelling case for Julian Anderson’s Incantesimi in its UK première and, at times in the Brahms, literally suspending the hall’s collective breath. No other orchestra is as globally familiar as this, thanks to its online presence and slick PR maching, but for a 21st-century brand to deliver such intimate and heartfelt performances as these last two nights fully justifies every bit of their success.

Anderson wrote his nocturne Incantesimi in 2015-16 to a commission from the Royal Philharmonic Society, Berlin Phil and Boston Symphony Orchestras, dedicated to Rattle. The 11-minute work features “five musical ideas in perpetual orbit”, through which we are guided by Dominik Wollenweber’s beguiling cor anglais solo. This rose out of some fascinatingly scored orchestral timbres in which the soundworld was more a delicate hum than anything else, with an indistinct fog of colours emanating from the horns and low woodwind. The orchestra’s skilful control in weaving together an array of unfamiliar textures and before delicately teasing them apart again was obvious.

The work’s late climax was striking both visually and aurally, with trumpets perched high above the stage to Rattle’s right, horns with bells aloft to his left, and two pairs of crash cymbals rolling abrasively at the rear. It is not often that a new work is as well received as this, notwithstanding its celebrity exponents, but Incantesimi is a work which demands to be heard again.

Rattle dispensed with a score for the remainder of the evening, conducting the Dvořák and Brahms in places with meticulous detail and elsewhere with just a gentle hand on the tiller. The promotion of Dvořák‘s Op.46 Slavonic Dances from encore fodder to concert suite proved a shrewd move, not so much in plumbing any particularly profound new depths, but in highlighting the sense of whole and even narrative arc which comes from playing them as a set. The playing was as technically flawless as expected, but the rich characterisation given to each movement, achieved through subtle changes in string sound and wind articulation, was a pleasing reminder of the diversity of these bucolic tunes. The glassy string textures and seamless woodwind lines of the slow movements were every bit as wonderful as the end-of-term high jinks atmosphere of the outer Presto movements.

I cannot recall ever having heard an account of Brahms' Second Symphony as thrilling and yet sonically refined as tonight’s. The overwhelming sense of joy at the end of the symphony boiled over into an eruption of applause even as the last affirmation of D major blazed from the stage. With last night’s Prom 65 fresh in the memory, it was easy to hear Mahler in the dewy opening moments of the symphony and the descending broken chords in the finale. The orchestral ensemble was plain for all to see in the very frequent glances and grins between desk partners and further across the stage, which no doubt helped establish the strong sense of clarity evident in the outer movements' rich details. The nominations list for individual excellence was a long one, but Stefan Dohr’s ensuing horn solos were a delight to behold throughout, particularly memorable late in the first movement, where there was an almost distressed edge to the sound, neatly teeing up a serenely redemptive slow movement.

The big tune of the finale started with a soft tread before erupting into a bounding Allegro, propelled forwards by fierce double bass accents and hard-sticked timpani playing. Latterly the opening theme returned at a whispered dynamic one would have thought impossibly soft for an orchestra a fraction the size of this, before the surging tide swept onwards. The last moments, heralded by those blistering descending trombone lines, were perfection.