The Metropolitan Opera’s new “Giulio Cesare” (1724), which opened last week, is a Handel production in its Platonic form. The funny yet poignant staging (originally from the Glyndebourne Festival) of David McVicar; the conducting of Harry Bicket, who knows better than anyone how to make a modern orchestra understand baroque music; and a top-flight cast, including countertenor David Daniels and soprano Natalie Dessay in captivating performances, made for 4½ hours (including intermissions) of musical and theatrical bliss.

Mr. McVicar shifts the Caesar and Cleopatra story into the era of British imperialism and then plays with it. From the red-coated soldiers to a quasi-Bollywood dance number (Andrew George did the hilarious choreography), all the theatrical ideas worked, and their arc captured the opera’s potent mix of wit and pathos. Robert Jones’s sets and Paule Constable’s lighting started with the baroque-theater perspective style, but dropped in sly additions; Brigitte Reiffenstuel’s eye-catching costumes kept pace, with everything from harem regalia and a spangled black cocktail dress to hunting garb and a riding habit. Big scenes, like Cesare’s aria “Va tacito,” staged like a stalking dance, were full of sharp details (the villain Tolomeo offering poisoned refreshments) that added up; serious, intimate moments, like Cleopatra’s heartbroken “Piangerò,” pulled us into the character’s emotion.

As Cesare, Mr. Daniels demonstrated that he is the master of this repertoire. He works harder in the florid passages these days, but every phrase hit the mark beautifully, and he made Cesare amusingly pompous as well as heroic. Ms. Dessay was astonishing, singing with lyricism, sparkle and some outrageous vocal ornaments—projecting Cleopatra’s emotional range from conniving flirtiness to abject despair, and dancing the Bollywood number and a hornpipe (“Da tempeste”) full out.

Also arresting were the countertenor Christophe Dumaux—precise, vehement and as agile physically as he is vocally—in the role of Tolomeo, Cleopatra’s nasty brother, and mezzo Alice Coote, eloquent as Sesto, who spends the entire opera swearing revenge for the murder of his father, the murdered Roman general Pompey. Mr. McVicar’s treatment of Sesto’s sometimes tedious obsession is an example of how cleverly he structured the evening; by the end, Sesto—with his monomaniacal mission achieved—has fallen into a near-catatonic state. Patricia Bardon took a while to warm up as Sesto’s much put-upon mother, Cornelia; debutants Guido Loconsolo as the general Achilla and Rachid Ben Abdeslam as the servant Nireno ably completed the cast.

The evening was paced with superb sensitivity by Mr. Bicket, who also played harpsichord. Every moment was full of life, with a constant awareness of the underlying pulse of the music and the breath between the notes; the orchestra and continuo felt like a cushion supporting the singers. The wrenching duet that concludes Act I, as Cornelia and Sesto are about to be dragged off to separate prisons, sounded like a series of sighs; and after hearing (and seeing) this version of Cleopatra’s victory aria, “Da tempeste,” one could never imagine it as anything but a dance.