Just when you thought you'd had your fill of vicious backstabbing and political assassination, along comes a Titus Andronicus. The third in the RSC's current season of four Rome plays by Shakespeare (we've already seen Julius Caesar and Antony and Cleopatra), Titus is far and away the bloodiest, goriest and most in-yer-face of the lot.

Traditionally, it's rarely done because of its high body count and endlessly imaginative methods of despatching victims, from dismemberment to baking, including pretty much all points in between. It's hard to strike the right tone without lurching into black comedy or relentless misery.

Here, director Blanche McIntyre treads the fine line with some deft footwork, indulging the audience in some nervous laughter while always doing the text the courtesy of taking it seriously. The result is, indeed, bleak, but never feels like an endurance test, even with a running time well over three hours.

She's aided considerably by the decision to stage the production in a parallel modern universe, where Rome is a self-destructive superpower run by a dissolute cabal of in-fighting narcissists. But once again, McIntyre sidesteps the potential for direct real-world comparisons and instead succeeds in offering a more general dissection of the dangers of blind honour, revenge and simple bloodlust. It's all the more powerful for the sweep of its targets, rather than making too specific and narrow a point.

Often, modern-day productions can seem gimmicky and overwrought with conceptual notions into which the Elizabethan text is uncomfortably squeezed. Not so in this show. Any contemporary device or prop is woven seamlessly into the language, rendering the 21st century setting both credible and highly resonant.

Among the performances, there are many developed characterisations, among them Tom McCall's bitter but judicious Lucius, torn between loyalty to his father Titus and his duty to the empire. Martin Hutson is simultaneously devious and naive as the power-grabbing Saturninus, eldest son of the previous emperor, whose naked ambition and egregious expedience spark the initial unravelling of the rollicking plot. And Stefan Adegbola imbues the villainous Moor Aaron with considerable dignity and pride, turning him from a one-dimensional baddie into a figure with justifiable motivations.

But the evening belongs to David Troughton, whose Titus is a fine and thoroughly enjoyable creation. From a starting point of soldierly stature and devotion to the state, he ranges through fury and bitterness to dark humour and Pyrrhic triumph as his world disintegrates around him and treachery unpicks his lifelong mission.

You always get the feeling you're in the safest of hands with this accomplished, ebullient actor, and he relishes every moment of his time on stage. Having played Gloucester to Antony Sher's Lear last year, you can't help wondering if he's using this production as a kind of audition for the main role himself. He's certainly got the depth, range and intellectual chops for the part.

Elsewhere, designer Robert Innes Hopkins' set – shared across the season – works extremely effectively, while Tim Sutton's music and Malcolm Rippeth's lighting add texture without getting in the way. Chris Fisher's illusions and the work of the makeup and props departments must also be credited for their effectiveness in the lasting impact of this production.

The second half runs out of steam a little, tending slightly more to the ridiculous (a naked Titus in a cardboard box?), and it might not be the greatest of Shakespeare's plays, but it's certainly given a breathless and mostly impressive outing here.

Titus Andronicus runs at the Royal Shakespeare Theatre until 2 September, then transfers to the Barbican from 7 December to 19 January.