Outside of a Nicole Holofcener film like “Enough Said,” you’ll never see a portrait of late middle age in an American film like Chilean actress Paulina Garcia’s performance in “Gloria.”

Playing a divorced 58-year-old woman reluctant to accept the image of a 58-year-old woman that others project on her, Gloria is still desperately reaching out to grab life. In the film, we see her get drunk, get high, bungee-jump, sing along with silly pop songs on the radio, and have satisfying sex with her elderly boyfriend. But we also see her deeply lonely side, ignored by younger men and women at parties, sitting alone at a hotel bar, trying to come to terms with the fact that her options may be dwindling.

Garcia weaves all this complex, at times contradictory colors into a wonderful character in a poignant film. “Gloria” never played theatrically in Madison, but it’s out on DVD and video-on-demand this week and is definitely worth seeking out.

Gloria is being forced to come to terms with the fact that the people in her life are slowly slipping away. She hardly sees her son, who lives in another city in Chile, and now comes news that her daughter, who she dotes on, is moving to Norway to live with her new husband. Meanwhile, Gloria’s relationship with her ex-husband is still tender — there’s a gorgeous scene where the family is gathered around the dinner table, looking at wedding photographs — but in the end, they’ve made their decisions and moved on.

Gloria takes up with Rodolfo (Sergio Hernandez), at least 10 years her elder, a kind amusement park owner still entangled in the life of ex-wife; if Gloria brings a suitcase’s worth of baggage to the relationship, Rodolfo has to rent his own handcart. Much of “Gloria” follows the relationship, as Gloria tries to make it work, knowing Rodolfo will never fill the void growing in her life, wondering if she can live with that.

Writer-director Sebastien Lelio spends much of the film just letting the camera linger on Gloria as she lives her life. She radiates pure joy on the dance floor or on that bungee jump, her face crumpling in other scenes as disappointment finally overtakes her sunny spirit. There’s one extraordinary, dialogue-free scene at a party, where Gloria’s daughter and her friends are singing along to the song. Lelio keeps Gloria in the background, a little out of focus, smaller in the frame than everybody else, left out. Then, finally, he puts her face in profile, in sharp relief. And this woman, for whom music is life, isn’t singing.

Gloria ends the film wiser about life but not necessarily happier than she started it. The illusions that both sustained her and deluded her have been discarded, and she carries a new, hard-won self-possession. It’s a conclusion that’s both deeply sad and triumphant, a contradictory endpoint that’s perfect for such an extraordinary film. Although it’s hard to leave Gloria behind when it’s over.