During a career of 16 years that spanned numerous East Coast hospitals since the late ‘80s, real-life nurse Charles Cullen confessed to murdering at least 29 patients with a fatal cocktail of drugs he dripped into his victims’ bloodstream. That figure was only his confirmed body count, however. As a title card suggests at the end of Tobias Lindholm’s shrewd and absorbing drama “The Good Nurse” — a Netflix original that just premiered at Toronto — the real number of his victims was predicted to be as high as a blood-curdling 400.

Hopping from one job to the next, the serial killer went undetected by the authorities, with his connection to the unusual deaths remaining as an open-secret suspicion at every facility he worked at. In order to avoid legal ramifications, none of the hospitals reported him — they just made him someone else’s problem, as the story of any corrupt institution goes.

The culmination of this unprecedented crime and tragedy is the subject of Charles Graeber’s 2013 book “The Good Nurse: A True Story of Medicine, Madness and Murder,” which screenwriter Krysty Wilson-Cairns (“1917,” “Last Night in Soho”) deftly adapts for the screen with a taut structure and an empathetic eye in her first solo effort. Cullen’s story is so shocking and scandalous that it could easily have become a trite white-knuckle thriller in lesser hands or an average season of a true-crime podcast like “Dr. Death.”

But Wilson-Cairns and Lindholm, the director of the elegantly restrained Danish films “A War” and “A Hijacking,” thankfully demonstrate early on that they have little interest in sensationalist run-of-the-mill embellishments. Instead they maintain a grounded focus on the immense shortcomings of the American healthcare system as a privatized and for-profit business with little regard for patient well-being. That choice pays off enormously in the end, with a memorable and emotionally complex political parting note.

Operating in new terrain for him, Eddie Redmayne plays Cullen, darkening his brand of amiable bashfulness with unsettling details. While the film’s brief, 1996-set opening sequence is all about him, as he watches the death of a patient in cardiac arrest with chilling indifference, Wilson-Cairns smartly constructs the rest of the story from the viewpoint of another caregiver. After this unnerving intro, we jump to 2003 to a modest New Jersey hospital, where Amy Loughren (Jessica Chastain, understated yet arresting) works as a kind-hearted nurse.

“The Good Nurse” swiftly spells out her moral traits in economical introductory scenes. For starters, we learn that Amy is a sacrificing single mother of two as well as a genuine nurturer at work, one who secretly lets her patients’ loved ones stay overnight (“I won’t tell if you don’t”), despite repeated reminders from her supervisor that times are tough, belts need to be tightened and they can’t afford to run a hotel for the relatives. We also learn about her life-threatening heart disease, requiring expensive surgery that Amy’s insurance won’t cover until further benefits kick in, in about four months.

It’s infuriating to witness the health struggles of the helpless Amy, who should normally be first in line to receive necessary urgent care as an indispensable caregiver herself. But Amy knows the unfair system inside out, well aware of the fact that she has to lay low and keep her condition a secret (otherwise she’ll be fired), until her insurance will cover her long-term disability benefits. It’s perhaps due to her exhaustion and powerlessness that Amy doesn’t keep a closer eye on Charlie when he first joins her shift as the hospital’s newbie, proving to be a quick study as well as a sympathetic companion to the overworked nurse.

The two quickly bond, with Charlie lending Amy and her kids a helping hand, respecting her secret and even nursing her with affection and stolen medication from the hospital stock. But when Amy’s patients, all drawn with humane touches, start expiring at random under her nose, she decides to partner with the police, especially once it becomes clear that the hospital would do anything to avoid liability amid growing suspicions of malpractice.

Redmayne mostly delivers a believably disquieting performance as the reserved murderer, save for an out-of-place outburst where he overemphasizes Charlie’s disturbed psyche. (Let’s say that if Redmayne were to get Oscar nominated with this role, the said showy moment would be his “awards clip” — it’s that scenery-chewing.) Chastain, on the other hand, is simply magnetic in a low-key role, more impressive on the whole than her flashy, Oscar-winning performance in last year’s “The Eyes of Tammy Faye”. Subtly projecting love, dignity and empathy, Chastain brings Amy to life as a flesh-and-blood do-gooder, especially shining in the film’s smaller moments as a sharp but vulnerable soul who needs to stop her friend from causing further harm.

Elsewhere, Nnamdi Asomugha and Noah Emmerich make sturdy impressions as a pair of hard-nosed detectives out of a retro cop drama, supplementing the procedural mechanics of “The Good Nurse” against the hospital’s antagonistic suit, capably portrayed by Kim Dickens.

“The Good Nurse” ultimately makes a sophisticated impression as a moving, deeply political human interest story, elevated by Jody Lee Lipes’ aptly icy, claustrophobic cinematography and an eerily chic score by Biosphere. What lingers most about it is a sense of selfless compassion, the kind that Amy possesses when she painfully reminds herself of the good buried within inexplicable evil. Watching her try to summon that good makes for a quietly devastating finale, one that’s thoroughly earned by the soulful film that precedes it.