7:34 PM PT -- Halyna Hutchins' parents and sister just reacted to the news of Hannah's conviction. Their attorneys, Gloria Allred and John Carpenter, say ... "Halyna’s parents and her sister have always wanted everyone who is responsible for Halyna’s death to be held accountable.Today was the first trial and conviction in the criminal justice process."

They add, "We are satisfied that the jury, based on the evidence, found Hannah Gutierrez-Reed guilty beyond a reasonable doubt for her part in the taking of Halyna’s life.We look forward to the justice system continuing to make sure that everyone else who is responsible for Halyna's death is required to face the legal consequences for their actions."

Hannah Gutierrez-Reed -- the armorer on "Rust" who was charged in connection to the death of Halyna Hutchins -- just lost her criminal trial ... 'cause a jury says she's guilty of a crime.

A verdict was just read in court Wednesday out in New Mexico, where Gutierrez-Reed has been on trial since the end of last month ... with prosecutors going after her on two different charges -- namely, involuntary manslaughter and evidence tampering.

She was found guilty of involuntary manslaughter, but not guilty of the alleged tampering.

A slew of witnesses were trotted out by the prosecution ... including the first assistant director, a producer on the film, and a line producer as well -- all of whom testified against HGR.

The prosecution's case basically amounted to Hannah being careless on the set -- to the point that it amounted to negligence, they claimed -- and it sounds like the jurors agreed after about a 2 week-long trial.

Hannah was remanded to custody ... meaning she was taken to jail right there in the courthouse -- this despite the fact that her attorneys asked she remain free until sentencing. The judge denied that ... noting a death had occurred, and that she'd been found guilty.

Hannah's family was sitting behind her during all this, and once the decision was reached that she'd be going behind bars immediately ... her loved ones started to break down.

Hannah herself remained stoic throughout the proceeding, and she didn't put up a fight as deputies led her away. A sentencing date will be set later down the line. She was facing up to 3 years in prison if convicted on both counts ... now, it'll be a fraction of that -- just up to 18 months in prison and a $5,000 fine. Unclear how much time she'll end up serving.

As we reported ... some key people testified against Hannah -- with Ryan Winterstern (a producer) going under oath to refute Hannah's claim that she'd asked for more armorer time while they were shooting the flick, specifically as it related to Alec Baldwin's cross draw.

Another producer, Gabrielle Pickle, testified that Hannah had ignored her complaints about weapons being left unattended on the set ... and that she allegedly shot down a logging system to see who was handling the guns and when. That was just some of the evidence.

Hannah's defense ended up basically boiling down to her being overworked by the production ... with her attorneys insisting Halyna being shot and killed wasn't on her whatsoever.

Clearly, a jury disagreed on that front ... but they didn't see enough evidence to convince them that Hannah had tampered with anything. No word on whether she'll appeal.

Of course, Alec himself still has a looming trial that'll kick off later this summer. He's facing manslaughter charges as well ... which he's pled not guilty to.