There's sometimes a slight sense of snobbery towards Shakespeare's early contemporary Christopher Marlowe, as if his youthful, passionate plays must inevitably be inferior to the mature work of the Bard. Fortunately for Kit, no such sense pervades this epic, eloquent production of his first play, brimming with iambic poetry and full of adventure.

Director Kimberley Sykes makes the most of her RSC debut, covering the Swan stage with fine brown sand in a triumphant design coup that informs everything else in the production. One moment it's the desert shores of Africa, another it's the ashes of a symbolic conflagration, and the dust it throws up from the actors' bare feet creates a constant atmosphere of misty exoticism.

That theme is reinforced by one of the most beautiful scores I have heard at the RSC for a very long time, courtesy of multi-skilled composer and musician Mike Fletcher – also in his first outing with the company. His contribution layers Mediterranean-infused motifs with percussive rhythms to weave a thrilling underscore to the action. Coupled with Ciaran Bagnall's moody lighting and Ti Green's visually sumptuous design, the effect is compelling, intense and constantly absorbing.

Sykes manages to generate a sense of danger that keeps you hooked throughout, even if the momentum flags a little in the second half. The narrative is set up at the start by the capricious, hedonistic gods Jupiter, Venus and Cupid, who then toy with the mortals' affections and desires, heedless of their ultimate impact and the tragic destiny they are preparing.

Thus the Trojan hero Aeneas finds himself washed up on the shores of Libya, where the naïve but alluring Dido rules over the city of Carthage with her sister Anna at her side. Cupid's intervention, at Venus's request, leads Aeneas to abandon his intended mission to travel to Italy in search of a new home, and instead sets him up for a doomed love affair that has implications not just for his own domestic situation, but also for the future of the Trojan people.

Marlowe's tale is clearly told, with Sykes's pacing judged to perfection – although a little trimming might not go amiss. Chipo Chung invests the eponymous queen with a well-placed balance of adolescent infatuation and regal stature, so that she can switch from ceremonial pomp to girlish giggles in the blink of an eye. It's yet another accomplished company debut.

Amber James is moving and credible as her sibling, and both speak the poetry with clarity and intelligence, while Nicholas Day looks to be having a ball in his all-too-brief appearances as the white-suited, white-haired Jupiter. Sandy Grierson's Aeneas is a restless, roving figure of inconstancy, vacillating between soldierly leadership and the tug of lust. Among the many strong supporting performances, Tom McCall is impressive as Aeneas's lieutenant Achates and Ben Goffe a delight as the mischievous little Cupid.

The RSC may be primarily dedicated to the work of that other chap, but his one-time rival comes out of this particular production rather well too.

Dido, Queen of Carthage runs at The Swan Theatre, Stratford-upon-Avon, until 28 October 2017.