Few TV shows turn the corner creatively speaking quite as quickly as “The Leftovers,” which with its fifth and sixth episodes has significantly raised the bar from where the show began, becoming a far more engrossing experience. Indeed, had the HBO drama started out with similar vigor it would have likely drawn a rave review from this quadrant, instead of the tepid response it received.

Producers Damon Lindelof and Tom Perrotta, working from the latter’s book, have been frittering around the edges of something interesting in the early episodes, but seriously struggled with conveying why the audience should give a damn about its characters despite the sobering nature of their situation. There’s also the little matter of the triggering event — the sudden disappearance of 2% of the world’s population, which some perceive as the Rapture.

Initially, the series was weird, even eerie, but not particularly engaging. Sure, there’s the Guilty Remnant — a cult that has sprouted up in response to such an inexplicable catastrophe — but their self-imposed silence only heightened a sense of frustration with the show.

Last week, however, saw the series deal with the brutal slaying of a cult member, highlighting just how fragile civility has become under these extraordinary circumstances. And the latest hour (and SPOILER ALERT if you haven’t watched) finally gave “The Leftovers” a vibrant pulse by zeroing in on how damaged even the ostensibly normal survivors are, as related through the prism of Nora Durst (Carrie Coon), whose entire family (husband and children) were among the departed.

Nora’s desperation to feel — something, anything — was searingly driven home by her hiring of a prostitute to shoot her, absorbing the brutal impact through a bullet-proof vest. The fact that her job includes interviewing those who suffered a loss seems especially sobering, especially after her emotional breakdown later in the hour while meeting with a spiritual guru (Paterson Joseph), who might very well be a gifted charlatan/huckster.

The power of Sunday’s episode notwithstanding — and the scene between Coon and Joseph is a beautifully played showstopper — it’s still not entirely clear “The Leftovers” can find (or perhaps more accurately, maintain) a sense of equilibrium. That’s in part because its central family — the sheriff (Justin Theroux), his estranged wife (Amy Brenneman) and their kids — remain among the least interesting personalities, although the budding relationship between the sheriff and Nora bodes well.

Still, this creative surge creates a greater sense of hope that there really is a firstrate if somewhat off-kilter series within this concept — poignantly probing grief and the often arbitrary nature of loss.

Perrotta flagged this aspect in HBO’s press materials, saying even he didn’t fully understand at first that the book “became an examination of collective grief, and I realized I was writing about a search for meaning in the wake of a terrible mystery.”

Despite initial reservations about the first course, “The Leftovers” has heated up, exhibiting the ingredients to become more than just your run-of-the-mill TV dinner. The disclaimer would be that based on past performance, viewers might have to settle for something of an uneven, hit-miss affair, meaning this rush of goodwill could just as quickly vanish.

Nevertheless, if we find ourselves looking back at “The Leftovers” and ranking it among great pay-cable dramas, the key juncture as to when that happened won’t be any mystery at all.