NEW YORK — Everyone knows someone like Penelope, the hair-tugging, chronically fibbing one-upper (Speeding ticket? “I have 99 speeding tickets. I was speeding so fast I broke the sound barrier.”) that Kristen Wiig plays on “Saturday Night Live,” or so she’s beginning to hear. Or maybe they’ve — you’ve — had a run-in with the gum-popping, eye-rolling, demanding megajerks; the chatty, bargain-hungry Target cashier; or an irritated armchair film critic like Aunt Linda, who mispronounces Scorsese but loves “Garfield: A Tail of Two Kitties.”

These are the oversize, wacky-yet-true characters that Wiig, 35, has used to build an audience as a star of “SNL.” Though her fans recognize the personalities, they may not recognize the actress, who disappears weekly in middle-agedly bad outfits and worse hairpieces. (If you’re waiting for a wig pun, stop.)

With the departure of Amy Poehler last month, Wiig has become, during only her fourth season, the most veteran female cast member on the show. Aside from standouts like Gilda Radner, “SNL” had not been known for developing female comedy brands until the Tina Fey era. In the last live broadcast, in December, Wiig appeared in every sketch but one. Though she may pop up as House Speaker Nancy Pelosi or the financial adviser Suze Orman when the show returns live next Saturday, she will most likely, at some point, put aside the impressions and take on a warbly voice and an ugly knit to play someone more everyday.

“There’s something about a Christmas sweater that will always make me laugh,” she said in a recent interview in a cafe near her home on the Upper West Side of Manhattan, which is woefully devoid of tacked-on flair.

So too is Wiig, who describes herself as shy and never thought of herself as funny — still doesn’t, in some ways.

“My personality, people don’t — they’re surprised when I tell them that I do comedy,” she said, sipping ginger apple cider. In a gray-and-black striped V-neck, very slim-cut black pants and woolly boots, with perfectly manicured, shell-colored nails and her hair tucked into a knit billed cap, she looked the polar opposite of the manic, tacky characters she plays. She looked tasteful and unassuming.

But over the last year — when Fey and others may have finally stiletto-stomped the masculine surprise at the notion of a funny woman — Wiig has emerged as a comic standout. On “SNL” and in films like “Knocked Up,” in which she stole her few scenes as an undermining TV executive, she cornered a character-driven humor that is appealing without being mean-spirited. Like Will Ferrell she is not winking at the audience.

“She has this thing that Lily Tomlin used to have,” Lorne Michaels, the “SNL” producer, said, “which is that her characters are never losers, or at least they’re not thinking they are. They have confidence; they think it’s going well.”

In a phone interview Poehler, her frequent writing partner, said: “Even though Wiig plays a lot of quirky, nervous characters, she’s really like a very solid person, like a real rock. I can depend on her personally, and onstage you just never are not afraid that Wiig is not going to nail it.”

Starting from Groundlings up

Wiig came to “SNL” from the Groundlings, the storied Los Angeles improv troupe that was home to Ferrell, Maya Rudolph, Will Forte and Lisa Kudrow. And she came to the Groundlings — and to acting — mostly on a whim.

In Los Angeles she tried one traditional acting class. “It was one of those very Method classes where you have to sit for an hour with your eyes closed and pretend you’re drinking, like, hot soup,” she said. She didn’t take to it. But a co-worker invited her to see a show of the Groundlings. “I’d never known anything like that,” she said. She began taking classes with the school and within a few years made the Sunday company, the junior team and, about a year later, the Main Stage cast.

“That place changed my life,” she said.

Even among the Groundlings talent, “she definitely stood out,” said Mindy Sterling, an actress (Frau Farbissina in the Austin Powers franchise) and a veteran Groundling who taught Wiig as well as Rudolph and Kudrow. “She has a very sort of subtle quality to her,” Sterling said. “It’s not that she necessarily was clever. She’s an observer, and she can mimic and then bring her style to it, and that was what was really mesmerizing. There was something very real and accessible, always a sense of ‘Oh, my God, I know who that person is.’”

She added: “You know what? She’s pretty. You don’t usually see pretty funny women; you see goofy funny women. And I think she is a goofy funny woman, but she’s very attractive. And my son” — for whom Wiig baby-sat — “loved her.”