You might be put off going to “We Need to Talk About Kevin” by the fact that it comes from Lynne Ramsay, whose 2002 film “Movern Callar” was well-nigh insufferable. But while it shares the brittle, almost brutally clinical sensibility of the earlier picture, it’s much more accessible and a good deal more powerful.

The film is a grimmer, icier variant of the story told in “Beautiful Boy,” about a parent’s grief and shame in the wake of a child’s unspeakable crime. Tilda Swinton, in another powerful turn, is Eva Khatchadourian, who moves with chipper hubby Franklin (John C. Reilly) from the city to a big suburban home when they have a child, Kevin. It’s clear fairly quickly that Eva is not the naturally mothering type. She resents giving up her career, and her attitude hardly improves when the toddler (Rocky Duer) proves a colicky kid who screams and cries incessantly—except, oddly enough, when Daddy is around. Things don’t improve much when Kevin has grown into a surly tyke (Jasper Newell) who takes perverse pleasure in tormenting his mother while playing the darling with Franklin. And by the time the boy has grown into a teenager (Ezra Miller), he’s become a frightening figure to Eva while easily manipulating his father into believing he’s normal, indeed extraordinary.

As might be expected, Ramsay lays all this out not chronologically, but in shifting time frames that are easy to cope with because of Kevin’s ages. There’s a fourth layer to things, however: a later time when Eva is treated as a pariah, obviously because Kevin has committed some horrible act that’s injured a great many families. In these scenes the shell-shocked mother must deal with public insults, including attacks on her shabby house, while taking a demeaning job in a travel agency. What Kevin did will ultimately be revealed, of course, but it’s hardly difficult to predict well in advance, though there are elements to it that may come as a ghastly surprise.

Most of the praise for the film will probably be directed at Swinton, and she’s certainly brings her talent for high-strung intensity to the role, contrasting Eva with Reilly’s low-key, jovial portrayal of clueless Franklin. But what really gives the film its punch is the chilling performance of Miller as the teen Kevin. The actor, who was charmingly comic as Andy Garcia’s son in “City Island,” is in entirely different mode here, projecting an icily menacing manner that allows him to take charge of every scene he’s in. Newell is almost as effective as the younger version of the bad-seed boy.

As with “Callar,” Ramsay is obsessively concerned with the texture and compositions of individual scenes, working with cinematographer Seamus McGarvey, production designer Judy Becker, art director Charlie Kulsziski, set decorator Heather Loeffler and costume designer Catherine George to capture the precise visual mood she’s after. The background score, combining original music by Jonny Greenwood and items chosen by Ramsay and Roy Stewart Kinnear, is deployed with equal care.

But despite the degree of control Ramsay exercises, what’s most likely to stick with you from “Kevin” is the portrait Miller draws of unfathomable malice and Swinton of tortured incomprehension at its depth. This may be Ramsay’s film, but it would be little more than an antiseptic exercise if the cast hadn’t realized so fully its fearless vision the human condition as acidic and cruel.