When Harry Kupfer's Der Rosenkavalier opened in Salzburg in 2014, Zubin Mehta was originally billed to conduct. That performance would have formed a partnership of operatic veterans. The 80-year-old Mehta is noted for the sophisticated playing he inspires, and Harry Kupfer, also 80, has reformulated his boundary-pushing style into something more classic. But it wasn't meant to be. Mehta was forced to withdraw when health problems arose, and the baton went to the superstar stand-in Franz Welser-Möst. Now that Kupfer's production has arrived in Milan, Mehta's name is once again on the playbill. That alone will draw an audience to an opera house where the conductor has long enjoyed legendary status. The fact the music is Strauss has been a cause for especial excitement.

Strauss has been in Mehta's bloodstream since his late teens, when he began studies in Vienna with the conductor Hans Swarowsky, who wrote part of the libretto for Capriccio after burgeoning anti-semitism forced writer Stefan Zweig to take a backseat in the project. Mehta gave us a taste of his Straussian approach barely three weeks ago, with an all-Strauss programme with the Filarmonica della Scala, the theatre's symphonic orchestra, in which the sound was characterised by sparkle and fizz.

Tonight's playing possessed those qualities and more. Waltzes were especially sublime – they spiralled, glittered and hung in mid-air – and when textures dissolved there was arresting lucid radiance. Spaciousness combined with poise in a rendition brimming with detail, from the punchy outbursts that punctuate the Baron's misadventures to the cooing sighs that underline Sophie's reticence. Mehta's refusal to treat these as episodic statements gave the playing its polish. The music unravelled in a spun-out yarn.

The title roles, largely unchanged from the original outing, were just as well delivered. Günther Groissböck's Baron Ochs is a virile dandy in the bloom of middle age – far from the elderly Teutonic Falstaff that we have seen in other productions. Initially, it seemed that such an eye-catching Ochs would deny us the work's central comedic element. Yet his characterisation was increasingly grotesque, with Groissböck painting a flawless picture of misguided conceit.

Ochs' gallivanting is accompanied by a series of waltzes, a Straussian joke which Kupfer's modern update bypasses. The dance may be anachronistic in the context of the drama's original 18th century setting, but it was commonplace by the 20th century of Kupfer's update. But the director goes a step further. Having Ochs strip to such luxurious music, or make clumsy advances on Sophie to an oom-pah-pah drive, provokes a much deeper belly laugh than would Strauss's enigmatic wisecrack alone. Groissböck's singing was a joy: bright, brassy and with the necessary dexterity to negotiate Ochs' quickfire patter.

Krassimira Stoyanova evoked Ochs' polar opposite as the noble Marschallin. Her rolling tone tone was ideal for the role's underlying nostalgia, and was particularly moving in “Da geht er hin”, a meditation on the fleeting nature of youth. While it is sometimes hard to buy into the Marschallin's romantic relationship with the young Octavian, one of opera's great trouser roles, Sophie Koch's portrayal made the tryst entirely believable. The sharp edge to her voice worked well for this yapping puppy of a sweetheart, and there was lovely bloom to her depiction of a gradual coming of age, with Octavian grasping the true transience of pleasure.

But when Octavian transforms into the bawdy chamber maid Mirandel – some convoluted gender play within the confines of a single role – the comedy really begins to spark. Koch's Mirandel was gloriously coarse, bolstered by a brilliant translation in the surtitles which effectively communicated her crude way with words. Such a full-bodied portryal made other roles light up in contrast, not least Octavian's lover Sophie, who was played with disarming sweetness by Christiane Karg.

Among the supporting roles, Benjamin Bernheim won the biggest applause for his highly Italianate cameo appearance as the serenading tenor. Further national stereotypes came in the form of Italian intriguers Valzacchi and Annina, so well delivered that even tonight's audience couldn't object. Thomas E. Bauer was a stern and effective police officer, while the chorus of children were artful in their summoning of chaos in Act III's great prank scene.

Kufper's judicious staging evokes 20th-century Vienna with a backdrop of silvery photographs. This design is allegorical, more interested in the opera's metaphysical plane than in creating a firm setting in time and place. The image of an imperial facade evokes grandeur for the comings and goings of the Marschallin's visitors, while a barren landscape provides a melancholic setting for her moments of introspection. The fragmentary sets are merely suggestive of space, adding an extra layer of detachment as they reconfigure to adjust the spatial dimensions. Only for the Prater inn of Act III does the background become lush, with Kupfer tapping into something earthier for the work's comic denouement.