★ out of four stars

Rated: R.

Five words I never thought I’d string together: Jennifer Aniston made me cry.

Only one tear actually spilled over a lower lid and down the cheek, but still. It might not be saying much to point out that Aniston turns in the riskiest, most emotionally naked performance of her career in “Cake,” but the anti-vanity leap she takes is big, brave and deserving of sustained admiration. She showed she had it in her, way back in 2002’s “The Good Girl,” but not since, till now.

We meet grim, puffy-faced Claire in a circle of frenemies, all members of a chronic-pain support group discussing the recent suicide of Nina, one of their own (Anna Kendrick). Like the thatch of uncombed hair hiding scars on her face and the Percocet that dulls the aftereffects of an as-yet-unexplained accident, Claire uses bitter sarcasm and casual sex to mask her throbbing psychological wounds.

She finds a bit of solace in kindred spirit Roy (Sam Worthington), seething with quiet rage over Nina’s abandonment of him and their small son. But her top co-star is Adriana Barraza in a landslide.

As Silvana, Claire’s cook, housekeeper, confidante and tough-love counselor, Barraza turns in a wise and understated performance. The chemistry between these two women tips the scales of what can safely be called a “little” movie from just OK to really good.

Speaking of chemistry, Aniston’s is wonderful with everyone else in the cast as well. The fetching, somewhat menacing specter of Nina pops up to tease Claire now and then.

Others making brief but meaningful appearances include Chris Messina as Claire’s ex, Felicity Huffman as a support-group leader who needs work on her own capacity to forgive, and Huffman’s real-life husband, William H. Macy, in a devastating cameo.

Director Daniel Barnz was previously best known for “Won’t Back Down” (2012), in which he faced the daunting task of attracting mass audiences to a film about a low-income mom and teacher fighting the system. (He somewhat succeeded; it got middling to good reviews.) Barnz and writer Patrick Tobin demonstrate impressive abilities to tug at heartstrings, but never yank them.

What does the film’s title have to do with all this? Something in the end, obliquely, but it doesn’t really matter. “Cake” isn’t a movie about events unfolding in mixed-up order to create a whole. It’s about the feelings that those events induce — grief, comfort, ghosts, memories, the facing of unbearable truths.

And it’s about Aniston. It’s all about Aniston, who may have been snubbed by Oscar but has already taken home a better prize: a new career path in mid-life.