Something quite remarkable happens to the Royal Philharmonic Orchestra when Charles Dutoit stands before it. A band which can sound – and look – disengaged is suddenly transformed when its Principal Conductor galvanises it. Still remarkably spry – the RPO celebrates its 70th birthday this year, but Dutoit is nearly a decade older – the Swiss conductor maintained superb control in a globetrotting programme that whisked us from Rome's fountains to St Petersburg's Shrovetide Fair via Bohemia's woods and fields, deftly adjusting the orchestral palette to suit each work.

Appropriately enough, Dutoit employed watercolour delicacy in the outer movements of Respighi's Fountains of Rome. Depicting the play of the water of four fountains at different times of day, the Valle Giulia Fountain at Dawn rippled in dappled light, while flute birdsong beguiled as the sun set over the Villa Medici. In between, Respighi in gloriously unrestrained Technicolor shone, the Triton Fountain dazzling in a fierce harp and percussion glare. Long before the Trevi Fountain was made an icon in Fellini's La dolce vita, Respighi had immortalised it in sound. Under Dutoit's steady hand, it grew to a monumental climax, the RFH organ giving a solid foundation.

Watercolours were replaced by oils for Dvořák's Cello Concerto in B minor. Before Gautier Capuçon had struck a note, Dutoit had set the scene; hushed horn throbbing with gentle vibrato, tender clarinet and mahogany strings all had distinctly Czech accents. Capuçon's 1701 Matteo Goffriller has a bold, immediate sound although its tone is on the dry, gruff side. The second movement was imbued with mournful tone and a fine sense of gravitas. This was a slow-burner of a reading, muscular and impassioned. Dutoit, in his enthusiasm, lost his baton not once, but twice, including an overhead manoeuvre which saw it fly in a pleasing arc into the front row from where Capuçon managed to retrieve it.

The cellist's clean articulation gave character to the finale's dance, although it felt perilously scrambled at one point. His rhapsodic rubato wasn't quite in synch with the clarinet, although the duet with leader Duncan Riddell was spot on – locked into eye contact over Riddell's music stand. Capuçon earned an appreciative pat on the cheek from Dutoit, ever the sensitive accompanist, before offering Pablo Casals' Song of the Birds as a wistful encore.

After the interval, acrylics were squeezed from the tube; big, bold blocks of colour required for Stravinsky's Petrushka. Where many conductors opt for one or other of the suites Stravinsky hatched, Dutoit gave us the complete ballet. Although there were no dancers, the narrative was vivid. Rigid, jerky movements – almost like a marionette – characterised Dutoit's conducting (where fluidity has been his watchword in Respighi). We were immediately tumbled into the Shrovetide Fair, bursting with ebullience. It was a masterclass in conducting, like one of those expensive watches where all the inner workings are exposed. Each tick, whirr and click of the score was visible in the orchestra, precisely cued, as the tale of the magician manipulating his puppets – Petrushka, the Ballerina and the Moor – unfolded.

The occasional beat was missed, there was the odd smudge in the cornet's Ballerina theme, but the RPO attacked the Russian Dance with such tremendous vigour that everything was forgiven. As the trumpet struck up the vision of Petrushka's ghost, one sensed Nijinsky in his clown costume, angrily shaking his fists. Powerful storytelling, masterly storyteller.