Murder. Suicide. Grand larceny. Puccini's triptych of short operas, two tragedies followed by a riotous farce, always makes for an evening of variety, with the potential for many snatches of greatness. Antonio Pappano is a fan - he recorded Il Trittico with the LSO in 1998, and featured Gianni Schicchi in his BBC series on Italian opera - and undoubtedly had a large hand in its being chosen to open the Royal Opera's 2011-12 season. (By the way, I reviewed Il Trittico in Paris last year - there's more about the operas in that review).

Pappano's performance on Gianni Schicchi was nothing short of exceptional. It's probably the best example I've ever heard of an orchestra perfectly following rapidly paced dialogue, giving space for the many singers to make every word clearly audible and extract every inch of comic possibility. As the farcical pace hotted up towards the end, the orchestra got ever more frantic but never overpowered the singers. Gianni Schicchi is a great ensemble piece: no chorus but a dozen minor parts of whom most are on stage for the whole opera. Under Richard Jones's impressive direction, the movement around the stage was riotously funny, the best moment being the desperate search for Buoso Donati's will, in the course of which floorboards are lifted and papers strewn on the stage from the attic of the room with Donati's deathbed, gloriously kitsch as a 1950s soap opera front room with ghastly floral wallpaper and tacky furniture.

Although it's mainly an ensemble piece, Gianni Schicchi also contains the evening's most famous individual aria, O mio babbino caro, sung by Schicchi's daughter Lauretta as she persuades her father to help save her intended Rinuccio from penury. Ekaterina Siurina sang it wonderfully with heart-melting smoothness, backed by a gorgeously lilting accompaniment. Francesco Demuro made a fine Rinuccio, with his paean to Florence Firenze è come un albero fiorito sounding generous and warm-hearted, albeit slightly spoilt by a closing high B flat that wasn't quite nailed. But the performance belonged to Lucio Gallo in the title role: Gallo played the suave, conniving lawyer with true Italian verve - you could see why the Donati family both loathed and were fascinated by him. From Gallo and the whole cast, this was a magnificent performance.

Gallo's personality is less suited to the tough bargeman Michele in Il Tabarro. His voice was lovely in the lyrical passages, but he didn't quite make me believe in the hard-edged violence of a taciturn man who murders his wife's lover in cold blood. Alexandrs Antonenko was the outstanding performer of this first leg of the triptych: urgent, infatuated and with a big voice. Eva-Maria Westbroek was thoroughly credible as the down-trodden wife, although her subdued nature was perhaps a shade overplayed, so her closing scream didn't really curdle the blood and her duets with Gallo and Antonenko didn't quite achieve lift-off. But the music did. Aided by a set that faithfully reproduced a Seine barge on a dark evening, Il Tabarro has an overall mood of darkness and tension, with moments of escape as the characters remember other, sunnier places, and moments of explosive release. The constraints of not overpowering his singers meant that Pappano's dynamics couldn't be quite as extreme as in his extraordinary LSO studio recording, but he came very close to matching it for sustained power and drama.

Following the murderous climax of Il Tabarro, Suor Angelica starts in apparently gentle and pastoral harmony, albeit punctured by some alarming religiosity. But we soon discover that all is not well as the action builds up to its climax, the tumultuous stand-off between Angelica, sung by stand-in Ermonela Jaho, and her terrifying Aunt Princess, sung by Anna Larsson. Both singers performed this superbly, leaving spines tingling (and an intense desire to do bad things to the evil Aunt).

I'm sure opinions will differ, but to my mind, the set for Suor Angelica was a slight misfire. Our sisters were portrayed not as nuns but as nurses in a childrens' hospital. The set was artistically executed and stunning to look at, but the concept didn't convince me: after all, it's precisely the isolation far from her child that has affected Angelica most. In place of the religious redemption provided by the dying Angelica's ecstatic vision of her son, we were shown reinforcement of the evil done to her as a child in her arms is dragged away once again. It all added to the bleakness - but it's not the ending that was intended by composer or librettist.

But as in the other two operas, the orchestral performance was remarkable. This time, it was in a different fashion: eschewing the lushness with which Puccini is often played, Pappano conducted Suor Angelica sparsely, giving lots of breathing space to individual instrumental phrases.

Il Trittico hasn't been staged in full at Covent Garden since 1965. I think it's been an omission: it's a set of works that makes for one of the best evenings of drama you can get in an opera house, and Pappano, Jones and the large cast played it to the full. It's not sold out yet, and deserves to be.