When William Goldman wanted to demonstrate economy in screenwriting in his book Adventures in the Screen Trade, he used a scene from Raymond Chandler: a husband and wife are travelling silently together in a lift, she carrying her handbag, he wearing his hat. The lift stops, the doors open and a pretty young woman gets in. The man takes off his hat – that brief, wordless scene tells you all you need to know about the couple and their marriage.

In a few, equally brief and wordless seconds, the opening scene of the debut episode of Killing Eve (BBC One) topples Goldman/Chandler’s example from its throne. A young woman in a cafe smiles at a little girl eating ice-cream at the next table. The girl does not respond, but smiles at the barista when he grins. The woman imitates the grin and the girl smiles back at her. The woman gets up, pays her bill and, as she leaves the cafe, tips the bowl of ice-cream into the child’s lap.

It is – narratively and dramatically speaking, at least – a classy move and one that sets us up splendidly for the stylishly ruthless hour to come as we get to know – via pitch-perfect performances by Sandra Oh and Jodie Comer across seven more binge-worthy episodes – the two protagonists who will end up playing cat and mouse across the globe.

The purveyor of casually exquisite child cruelty is Villanelle (Comer) – a proficient, prolific and pitiless assassin; think Nikita without a conscience and free to revel in her work. She keeps her bullets in a drawer next to her tampons and depilatory aids, and likes to relax with the occasional threesome and by faking her death in her handler’s apartment. By the end of the episode, she has used a small boy to lure his grandad away from a Tuscan wedding so she can stab him through the eye with a poisoned hairpin, nipped to London to slice a visiting Russian politician through the femoral artery and laid waste to half the hospital guarding the Polish girlfriend who was the only witness to his murder.

Proficient, prolific and pitiless … Jodie Comer as the assassin Villanelle in Killing Eve. Photograph: Sid Gentle Films/Robert Viglasky

MI5 agent Eve (Oh) has already intuited that the murderer is someone the misogynist politician would not have seen as a threat. Bored to tears by her deskbound duties, she starts to investigate inconsistencies in the case and is fired by her “dickswab” boss for her trouble. She is soon approached by someone higher up the espionage food chain with an offer to continue as a more secret secret agent.

Killing Eve was adapted from Luke Jennings’ novels by Phoebe Waller-Bridge, the creator of the darkly flashing gem Fleabag, and her presence runs through it like a stick of rock. All her biting intelligence and idiosyncrasies, everything that made Fleabag great, are here (and Villanelle is Fleabag’s protagonist with just a couple more deviant pairings in her DNA). Just as Fleabag subverted sitcom expectations with its naturalistically scabrous dialogue, so the conventions of the spy genre are here twisted into something new. Partly by the fact that, per Jennings’ books, both leads are women. Traditionally, they are only allowed – see your Jane Tennisons, Stella Gibsons, Robin Griffins – to be the pursuer, not the pursued, intent on bringing the aberrant latter to justice.

But on top of that there is the snapping, crackling script – the perfect command of comedy and tragedy, and the turns to and from each, the approach to every moment that is just 10 degrees off centre and characters so fully developed that even the second-stringers can pull off self-reflexive jokes. When Eve’s off-book investigations come to light, her boss (the wonderful David Haig being customarily wonderful) notes: “You could get into a lot of trouble if I was a serious man.’

And it wears its feminist credentials so lightly. Eve doesn’t have to fight any overt sexism. Her boss and husband are good, supportive guys. She is just frustrated by her job and a life that hasn’t quite panned out as she had hoped. Just like … a person. Villanelle only uses her femaleness to get physically close enough to slice, stab or shoot her victims, not seduce them. She and Eve are drawn to each other not because they are both women in a man’s world, but because they have, as individuals long underestimated in their respective fields and longing for a challenge, so much in common.

This isn’t a retrograde step. This is progress. This is a stance that says we are at a point now where creators do not have to apologise for or drag in contemporary hot-button issues to justify writing about women. It can just be done. This is both what normalisation means and how it is consolidated. And we will, for the next seven weeks, have such fun along the way.