The Times said the ex-West Wing star is "quite brilliant" in Apologia, in which she plays an art historian at odds with her two sons and their partners.
According to the Daily Telegraph, the 73-year-old "beautifully lets a lifetime of hurt seep through [her character's] brittle facade".
Downton Abbey's Laura Carmichael also appears in Alexi Kaye Campbell's play.
First staged in 2009, the piece has been reworked to accommodate an American lead actress.
Its opening this week comes amid reports that NBC is considering bringing The West Wing back to TV screens.
Channing played First Lady Abigail "Abbey" Bartlet in the White House-based drama, which originally ran from 1999 to 2006.
Apologia - whose title is defined in the play as "a written defence of one's opinions and conduct" - sees Channing's character, a former '60s radical, clash comically with her son's respective girlfriends over a birthday dinner.
One, played by Carmichael, is a fervent Christian, while the other, played by Doctor Who's Freema Agyeman, is a materialistic soap actress.
Speaking ahead of Thursday's press night, Channing described her character as "a feminist and a scholar with a bit of a rebellious streak".
"She's very smart, extremely witty and she's not very diplomatic, so there's a lot of wonderful language," she told the BBC.
One of the biggest laughs of the evening comes when Carmichael's Trudi character expresses optimism over the nascent presidency of Barack Obama.
"Let's wait and see how things turn out in the long run before we start jumping with joy," replies Channing's Kristin presciently.
"Things rarely turn out the way we expect or how we hope," says Channing, going on to make her own comparison between Obama's tenure and what has followed.
"We could do with a little grace, a little diplomacy, self-control, discretion - the list goes on," she sighs in reference to the White House's current incumbent.
Appetite for more West Wing remains strong, stoked in part by a popular podcast - The West Wing Weekly - that dissects the show episode by episode.
Yet Channing does not believe the Aaron Sorkin-scripted drama will emulate the likes of Will and Grace and Roseanne and mount a comeback.
"I don't think it will return," says the actress, whose other famous roles include Rizzo in 1978's Grease and Julianna Margulies' mother in The Good Wife.
Speaking on Thursday, Alexi Kaye Campbell said he was "excited" Channing had crossed the Atlantic to appear in his play.
He told the BBC he had intentionally written the play in response to a perceived lack of roles available for older female leads.
"Before I wrote the play there was a constant conversation about not enough parts being written for older women," he said.
"Most of the most interesting people I know are older women, so that was something I wanted to consciously address."
Writing in The Guardian, critic Michael Billington described Channing as "a serious, intelligent actor [who] induces sympathy for the character of a seemingly monstrous matriarch".
Yet he took issue with what he called Kristin's "astonishing insensitivity" and questioned Campbell's "assumption that left-wing militancy is incompatible with good manners."
Channing last appeared in the West End in 1992 in Six Degrees of Separation. She went on to star in the film version of John Guare's play, for which she was nominated for an Oscar in 1994.
Since then she has been seen in London in The Exonerated at the Riverside Studios in Hammersmith and Awake and Sing at the Almeida theatre is Islington.
Apologia runs at London's Trafalgar Studios until 18 November.
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US actress Stockard Channing has been praised by critics for her first West End appearance since 1992.