The one thing that keeps you on the edge of your seat for the sober-minded thriller “The Only Living Pickpocket in New York” is the suspense over how good the finale will be. Because so much that’s preceded it — from the casting to the down-market Bronx settings, the music (Bobby Short and “You’re a Native New Yorker”) to cruel youth vs. world-weary age conflict at the heart — is damned near perfect.

The is a genre picture brimming with character and grit. And it soon becomes clear that the finale will be the only chance that writer-director Noah Segan (“Blood Relatives” has to blow it. Which he kind of does by overreaching, sentimentalizing and stripping away mystery from all that’s come in the first 80 minutes by trying too hard to tidy things up in the end.

John Turturro has that rare role worthy of him as Harry, a veteran thief who rides the (subway) rails and prowls the streets picking out his next mark. Harry’s good at blending in — salt and pepper hair, beard and overcoat. We’re introduced to him by following that first mark through the opening credits. When the well-heeled Manhattanite stands next to the wrong tall Italian on the subway, it’s bye-bye billfold.

But this is the 2020s. It’s a cashless society. Stolen phones are only worth anything to “the Chinese guy” on the edge of the Village. Watches? Who needs them, and who will pay top dollar for genuine Swiss movement when a look-alike knockoff is as near as the next street corner.

Steve Buscemi is Harry’s wizened pawnbroker/fence Ben, the one who reminds him he’s a dinosaur and that street pickings aren’t worth what they once were.

Harry runs into a former protege (Victoria Moroles) who is all about cyber hustles these days. “You gotta learn new tricks,” she says. Nope. There’s nothing like “the old ‘five finger discount,'” the master pocket picker insists.

Harry’s taking care of his catatonic wife (Karina Arroyave), and generously tipping nurses’ assistants and neighbors who pitch in. He knows how this city works. A homeless person he asks for directions has her hand out. So does everybody else.

Then his shrinking world is upended when he sets up and breaks into a pretty boy’s (Will Price of TV’s latest “Goosebumps,” and “Eleanor the Great”) ’69 Barracuda. Harry’s not just good at picking pockets.

But rummaging through that kid’s gym bag turns up a pistol — a tell. There’s also a wad of cash and a flash drive, which Old School Harry knows nothing about and Ben, with his Radio Shack era pan shown PC, has no means of opening.

Might the streetwise pickpocket be a match for the “Ivy” educated punk running his own gang, a kid from a Jersey “family” that’s not to be trifled with? Harry’s lack of tech savvy and his routines make him far too easy to track down. Now everybody in his world is in the same fix he is.

An intimate, edgy New York tale like this one would count itself lucky to land Turturro or Buscemi to give it authenticity. Here, actor-turned-director Segan (he was the cop in “Knives Out”) and producer Rian Johnson get both, with the great Giancarlo Esposito as a playful, retirement-ready cop who’s crossed paths with Harry enough to joke around with him on the subway as he shows him cards with criminal suspects’ photos on them to see if Harry might inform on where they are.

Price is something of a “find” — playing a good-looking college man too polished to be openly sadistic, but blunt about Harry’s fate if that flash drive isn’t back in his hands, pronto. “Dylan” is scary not because he’s violent and tough, or because he’s connected enough to have a crew to do his dirty work, but too smart to leave everything to a bunch of mugs.

Turturro’s Harry is a criminal with a humanity that comes with age, returning cash-free wallets via mailboxes, not begrudging his victims’ modern ways of avoiding cash with an “Even suckers get a day off, sometimes.” Heartless Dylan is amoral, impulsive, violent youth incarnate — capable of anything to get what’s his and not be made a sucker by a pickpocket who might be in AARP.

Segan’s lean, compact thriller takes care of business for a solid 80 minutes. And then he introduces new characters, flashback plot twists and scene after scene that simply does not have to be here, unless the financing was dependent on squeezing in an actual Oscar winner with three guys who ought to have one themselves.

I still loved the adult nature of the story — older people with grave responsibilities and shortcomings like falling into dangerous, out-of-step-with-our-surveillance-state times habits, generosity, loyalty, family neglect and self-preservation that keep coming back to bite them where it hurts.

“You old guys. You’re all about keeping your word.”

“That’s what makes it valuable.”

The acting is in-the-pocket, all up and down the line. Bit players like Echaka Agba, Kelvin Yan Hee, Mark Cayne and Lori Tan Chinn make vivid, lived-in impressions in tiny roles, as does Aida Turturro.

But watch this little gem of a thriller and tell me I’m wrong about the contortions the script undertakes to get to a few last twists and deliver a couple of extra, pithy conversations. If the fade to black with Bobby Short singing “I Happen to Like New York” had happened five minutes sooner, this would’ve been a jewel of this year’s awards season.

Rating: R, suggestions of violence, profanity

Cast: John Turturro, Steve Buscemi, Will Price, Victoria Moroles, Tatiana Maslany, Giancarlo Esposito and Jamie Lee Curtis

Credits: Scripted and directed by Noah Segan. A Sony Pictures Classic release.

Running time: 1:26