You can do anything with a face on screen these days, whether it’s shaving decades off with a digital scalpel or deepfaking it into unrecognizable oblivion. Usually this wizardry has the air of a stunt, a transformation pulled off merely because it’s possible. Never, however, have such effects proven as chillingly essential as they are in “Welcome to Chechnya,” a vital, pulse-quickening new documentary from journalist-turned-filmmaker David France that urgently lifts the lid on one of the most horrifying humanitarian crises of present times: the state-sanctioned purge of LGBTQ people in the eponymous southern Russian republic. Closely charting multiple missions to extract and protect brutalized victims of the regime, France collects the candid first-person perspectives that have proven difficult to come by in this climate of terror — thanks in large part to face-altering technology that keeps their identities hidden, but not their searing truth.

Premiering in competition at Sundance — with a Berlin date to follow, and an HBO release scheduled for June — “Welcome to Chechnya” further establishes France as America’s foremost documentarian on LGBTQ issues, following 2012’s superb, Oscar-nominated “How to Survive a Plague” and 2017’s similarly stirring “The Death and Life and Marsha P. Johnson.” His third feature represents a departure, however, from those historical, archive-trawling studies, instead taking the form of an anxiously in-the-moment docu-thriller, tracking and braiding the escape narratives of several human subjects in the present tense — often without tidy resolution or catharsis. This isn’t a story to reflect on, as Putin-directed Chechen authorities continue to flatly deny the human rights violations under scrutiny: This necessarily upsetting film aims for immediate awareness and action.

The pre-existing material in “Welcome to Chechnya” is by far its most distressing: grainy cellphone and surveillance camera footage of real-life homophobic attacks in the republic, including a gay couple confronted mid-kiss by a gang of jeering men, and a young woman dragged from a car and bludgeoned by a male relative in an apparent honor killing. These horrific flashes regularly punctuate the action, emphasizing the constant peril faced by its Chechen subjects. The first of these, 21-year-old Muslim lesbian “Anya,” is introduced via a desperate phone call to David Isteev, a journalist turned crisis response coordinator of the Russian LGBT Network: an activist group that arranges for endangered people like Anya to flee the region, sheltering them in safe houses around Europe.

Blackmailed for sex by an uncle in return for keeping her sexuality a secret from her father, Anya is just one cruel man’s whim away from being another casualty in Chechnya’s rapidly swelling list of LGBTQ people killed or forcibly disappeared in the last three years. Using a New Yorker exposé by Masha Gessen as his starting point, France claims the hate campaign escalated with a 2017 drug raid in which explicit gay images and messages were found on a suspect’s phone, thus initiating a chain system in which LGBTQ detainees are violently coerced by police into revealing the identifies of others.

It all amounts to a social “cleansing” project by Chechnya’s head of state Ramzan Kadyrov, a gun-loving far-right thug who denies the existence of such a campaign as vehemently as he denies the existence of any gay people in his republic at all. “We have no such people here,” he cheerfully tells U.S. sportscaster Bryant Gumbel in an excerpted 2017 interview. “To purify our blood, if there are any here, take them.” It’s clear Kadyrov gets his fake-news credentials from his Russian superior Vladimir Putin; the system that Isteev and his fellow activists, including grittily determined lesbian Olga Baranova, find themselves up against is in such profoundly corrupt denial, it’s all but impossible to fight.

France and co-writer/editor Tyler H. Walk trace these institutional battle lines with compelling rigor, but the heart of the film, in all senses, is with the survivors retrieved by Isteev, Baranova and their colleagues. In sequences more racked with nail-digging tension than any fictional prison-break film, France’s camera unobtrusively follows the activists on their runs into and out of Chechnya, complete with subterfuge, disguise and breath-halting border crossings. At a shelter in Moscow, we observe both the sense of community and alienation felt by the fugitives, some of them mere teenagers, after leaving everything in their former lives behind. For some, the exhilaration of escape only lasts so long before desolate fear of the future sets in, and the film seeks no pat feelgood shortcuts. One traumatized young man attempts suicide; for Anya, isolated indoors for her own safety in an undisclosed location, the lack of outside-world contact only aggravates her fragile mental state.

The closest thing here to an uplifting arc is still raddled with uncertainty and compromise. Having been detained and tortured while working in Chechnya, gay events planner Maxim (initially introduced as “Grisha”) is released on the strength of his Russian citizenship, only to be pursued once more when authorities fear he’ll tell his story to the media. (His family, in turn, is threatened, forced to flee their home.) United with his boyfriend in the Moscow shelter, Maxim resolves to take his case to the courts — becoming the first survivor to testify about the Chechen purge.

In parallel with this disclosure, he becomes the only subject in the film to let slip his real name and his digital mask — one of several deftly applied by VFX supervisor Ryan Laney, with only fleeting blurs and seams to betray the illusion. The dissolution of his computerized face, in the midst of an impassioned press conference with Russian media, is the one gasp-inducing moment of showmanship in a film that otherwise deploys clean, no-fuss shooting and cutting to gripping effect. Otherwise, the only flashes of cinematic artifice come via the cold, quick pulse of Evgueni and Sacha Galperine’s score at the most white-knuckle moments in proceedings.

Maxim’s story gives “Welcome to Chechnya” its clearest moments of emotional release, but needless to say, his testimony hardly has a seismic effect on a crisis this crushingly entrenched — with only limited awareness and support from the rest of the world. France’s film closes on a grimly telling statistical postscript, noting that of 151 survivors rescued by the Russian LGBT Network and granted refugee status in other countries, the Trump administration has accepted a grand total of zero. The ironically inviting title only hints at part of the story in this wholly devastating documentary: The crisis, it turns out, is all around us.