Straight off the bat, I tell Mary Elizabeth Winstead that she looks like crap in her new film. Those crushed eyes squinting out of a waxy face, the hair like oil-slick seaweed, the rag-doll posture. She takes it rather well. "This was not the movie where you wanted to be spending hours in makeup," she says. Or minutes, come to that. The film is Smashed and the smashee in question is Kate, a Los Angeles primary school teacher failing miserably to keep her alcoholism under wraps. In the first scene, she wets the bed. Dozing beside her is her husband (played by Breaking Bad's Aaron Paul); he is also an alcoholic, which explains why his response to waking up in her urine is very much in the "Oh, you!" vein. Kate takes two bottles into the shower instead of one, then it's off to work, where she swigs from her hip flask before vomiting in front of a class of six-year-olds. And that's just the opening 10 minutes.

Winstead, who turned 29 recently, couldn't be any more different in person. Her manner is chirpy, her look best described as regal-businesslike: brown hair tied back, black boots and trousers, a pistachio jacket worn over a high-collared white blouse with a conspicuous gold necklace. If the ensemble isn't very Smashed, the venue is – we're in a drab room in an office overlooking a stinky Soho street market. Somehow this suits her recent change in direction. She has not previously been known for low-budget indies. Together with Roman Coppola's A Glimpse Inside the Mind of Charles Swan III, in which she stars with Charlie Sheen and Bill Murray, Smashed is something of a new leaf.

Winstead isn't a household name, except in households with a subscription to Fangoria magazine. But if she is recognised at all, it is from multiplex sequels with football-score titles: Die Hard 4.0, Final Destination 3, The Ring 2. She was essentially a female Kurt Russell in the prequel to The Thing, and she played the First Lady in Abraham Lincoln: Vampire Hunter, the markedly less prestigious of this year's Lincoln movies. She donned a yellow cheerleader outfit for Quentin Tarantino's exploitation homage Death Proof and played a roller-skating, kickboxing dreamgirl in Scott Pilgrim vs the World. She will soon be seen fleetingly in A Good Day to Die Hard, reprising her role as Bruce Willis's daughter, but her heart belongs to Smashed.

"I really didn't have any fear about the humiliation factor," she says. "That was something I was excited to get the opportunity to explore. My fears were about pulling it off." Her extensive research included attending Alcoholics Anonymous meetings for several months. "I came into it very quietly: I didn't say I was an actor. If they asked me to speak, I'd tell them I had come to learn about AA. I never pretended to be anything I wasn't. But I also didn't want to stand up and say: 'Hey guys – I'm making a movieee! Anyone wanna tell me their story?'"

Her empathy for the character is unwavering, whether she's rallying herself unconvincingly for her pupils or staggering down the street after waking up on a discarded mattress. One particular scene stands out: Kate's breakdown after being refused alcohol in a convenience store. The scene ends with her sobbing as she urinates on the floor. "Most of the work in that scene is done before you get on set," she explains. "It was all to do with Kate reverting to a point in her childhood when she wanted something really badly but couldn't have it. As a little kid, you'll try everything. You go from cute to cross, you start throwing things and then you burst out crying. She's reaching back to that."

Winstead thinks the entertainment industry still fosters alcohol and drug abuse. "It's woven into the fabric," she says, "so you never really have to stop that behaviour." Making Smashed has changed the way she looks at the problem. "I used to see young people in the industry and think: 'They can't be alcoholic – they're just having a good time.' Then you ask yourself: 'Why don't I ever see them sober?'" Would she intervene now? "There's not much you can do, I think, unless they want help." You could slip them a DVD of Smashed. "Right," she laughs. "'Hey, did you see my new movie, hint-hint?'"

It's the enablers, she says, who make things worse. "If you have a problem and you're also successful, everyone does whatever they can to keep it going. I see that a lot. There'll be someone really famous and you'll hear their assistant saying: 'Oh, I have to go get their cocaine to get them out of bed.' I'm continually shocked, because I tend to think that stuff is consigned to the 1980s. I'll hear younger actors talking about drugs and I'll think: 'What? You? No!'"

Winstead believes her conservative upbringing shaped her straight-arrow habits. She was raised in Sandy, Utah, a suburb of Salt Lake City, the youngest child of five; her parents were religious, though not Mormon, and fiercely overprotective. "I wasn't allowed out anywhere. I had two friends. That was it. But I was also terrified of hanging out with other teenagers and going to parties. I didn't fit." She gravitated toward acting and dancing around the age of nine, and was working professionally by her teens. "I put my energy into that and never deviated from that path."

Her mother accompanied her to auditions and acting jobs in Los Angeles. They were installed at the Oakwood apartment complex, a haven for child actors and their parents. "When I stayed there, Hilary Duff was there, Frankie Muniz [Malcolm in the Middle] was there. Pretty much every famous kid lived there." So you found some friends at last? "Well, they all hung out together," she laughs. "I wasn't cool enough for them. Part of me was looking at them thinking, 'They're having so much fun.' But imagine if I'd gone along and they'd been drinking and smoking pot, they would have considered me nerdy and dull for not doing it." Suddenly I understand some of the anxiety she brings to Kate in Smashed: part of the character's dread of being sober comes, as Winstead points out, from "the fear that she will be boring without alcohol".

Her career picked up quickly. She didn't exactly seek out horror films: those were just the sort of parts available to young women, though she drew the line at oversexualised characters ("I've never felt comfortable playing them"). She became pigeonholed, unfairly she thinks, as a Scream Queen. "I don't feel I ever really played that part. Final Destination 3 isn't about running away screaming 'Don't kill me!' It's more like an action disaster movie." I enthuse about her grisly demise at a drive-thru restaurant in that picture, but it turns out I've got my spectacular death scenes mixed up. "No, I didn't die," she insists gently. "Or rather, it's open to debate." I confess that I can't even remember how many Final Destinations there are. She's a bit fuzzy on the subject herself. "Are there already six? Or is it the sixth one they're making now?" (It is.)

With Michael Cera in Scott Pilgrim vs. the World. Photograph: Kerry Hayes

Despite the picture she has painted of herself as a Billie-No-Mates, she has lots of friends now, as well as a husband (the film-maker Riley Stearns, whom she married in 2010), though she says it was only three or four years ago that she finally felt at home in LA. I don't know if celebrity will come to her, and I doubt she cares. She had a brush with it the last time I saw her, at Comic Con in San Diego in 2010, where she was mobbed by fans during the hoopla over Scott Pilgrim vs the World. "Everything was nuts," she marvels. "All of us from the movie were saying: 'Wow, we'd better prepare ourselves. Our lives are really gonna change.' Then the movie came out and it didn't do well. The gulf between expectation and reality was kind of funny. I was like: 'Oh. OK.'" She sounds almost relieved. As an outsider for so long, how would she have coped with unanimous acclaim? After Smashed, she's going to have to find out.