If you have an image in your head of orchestral musicians diligently following the lead of a conductor beating time, when it comes to Christian Thielemann conducting the Staatskapelle Dresden, you can forget it. Thielemann is clearly confident that his orchestra is going to play in time and at the right tempo: what he's doing on the podium is to fine tune – an "up a bit" or "down a bit" on the volume here, a slight gesture of "hurry up please" there.

And the confidence is totally appropriate. The Staatskapelle's string section sounds like a giant string quintet (or sextet or octet, depending on how Bruckner has split the strings), so tightly together are the players on each desk. Watching the double basses, you realise that every body movement is just as synchronised as the music sounds. Where the strings of lesser orchestras struggle to be heard in the Royal Albert Hall, the Dresdners sound effortlessly simple: clear notes with a lustrous sheen. Thielemann's continual attention to the dynamics pays dividends as phrases are given a complex contour – the rise and fall of the music happens on a micro scale as well as on the grand Brucknerian sweep. When, in the third movement scherzo of the Symphony no. 3 in D minor, Bruckner lets his hair down into a bit of Austrian Ländler, the music lilts and rocks us.

Individual instrumental virtuosity abounds. Every woodwind instrument shines clear and unwavering above the orchestral wash, with a splash of colour at the end of long-held notes. The timpani has exceptional evenness in the long rolls as well as the richest of sounds, perfect for Bruckner's go-to method of thickening the texture: a string swell, then brass entry, then timpani rolls. The symphony was composed when Bruckner was very much under Wagner's spell (it's often called the Wagner Symphony). Although the version played tonight was the 1876-7 Nowak version, in which most of the direct Wagner quotes are removed, the music is still suffused with the Wagnerian development of motifs and the use of brass to intensify them. The Staatskapelle's brass players left nothing to be desired: the return of the main trumpet theme, late in the first movement, was particularly exciting. When brass was called upon to combine with strings at lower volumes – there's a particularly lovely horn and strings interlude in the first movement – the balance was inch perfect.

Just as eagerly awaited as Thielemann and the Dresdners was Daniil Trifonov, the soloist for Mozart's Piano concerto no. 21 in C major. This may not be natural repertoire for Trifonov, from whom we've mainly heard later and Russian music, but his qualities were still evident: perfect legato, super-clear articulation. I was particular struck by a passage in the third movement where the pianist switches from a quavers to semiquavers. Suddenly, Trifonov was playing twice as many notes, but he was able to do so without even a fractional change in tempo or dynamics – an exceptional level of control over his instrument. The result was a performance of grace and poise. 

Mozart's opera was famously accused of having too many notes: a pianist might accuse the Andante of this concerto of having too few, the sheer simplicity of its gentle melody meaning that the soloist has to invest every note with significance. Trifonov did this with beauty and with a seriousness that belies his sense of impish humour, which comes through every time you hear him interviewed. That humour, however, came through in the cadenzas, written by Trifonov himself and ranging delightfully over the themes of the rest of the concerto – Trifonov having to recover from a near car crash just before the beginning of the first. An encore, from Prokofiev's Cinderella, was delicate and also witty.

Thielemann and the Dresdners gave fine accompaniment in a traditional, Karajan-like big-orchestral-sound sort of way, displaying the string sheen and the fine control of dynamics and phrasing that was to become even more evident in the Bruckner. This is a top class orchestra, and it's the first time that Thielemann has conducted at the Proms. I can't imagine what took them so long.