“Baby Mama” is not just smart, warm, funny, and romantic, it is an especially welcome dose of XX chromosome humor in an Apatow-flooded XY era.

Tina Fey (“30 Rock”) plays Kate, a single woman who has achieved a great deal of professional success as an executive in an organic food company but at age 37 finds herself overcome with longing for a baby. When her doctor (John Hodgman, the PC in Mac commercials) tells her that it is almost impossible for her to have a child, she hires a surrogate (“Saturday Night Live’s Amy Poehler as Angie). Shortly after she becomes pregnant, Angie leaves her husband and Kate, worried about Angie’s health and hygiene habits, eager to share the prenatal experience, and something of a micro-manager, invites her to move in. Think The Odd Couple with Lamaze class. We know that as must always happen in movies Kate will teach Angie about responsibility and Angie will teach Kate to loosen up and have a little fun. But it is done with a light touch and a sense of humor about itself, Fey and Poehler have an easy warmth and chemistry, and it feels good to see a buddy comedy about women.

Writer/director Michael McCullers (of “Austin Powers” and neglected gem Undercover Brother) wisely lets the characters lead the story, avoiding the usual wacky plot contrivances. Kate continues to be very successful at her job, and when Angie meets Kate’s boss, there are none of those tiresome and painful mix-ups/inadvertent insults/clumsy accidents that have to be corrected so that everyone can agree how much happier they are. Even better, McCullers fills the screen with top comic talent so that every encounter Kate and Angie have is, well, pregnant with possibilities that, well, deliver. Sigourney Weaver is magnificent as Chaffee Bicknell, the steely operator of the surrogacy company. When Kate expresses surprise at the $100,000 price tag — “It costs more to have someone born than to have someone killed,” Bicknell purrs sympathetically without losing a beat “It takes longer.”

Dax Shepard is unabashedly trashy as Angie’s husband (“common law!”), Maura Tierney adds warmth as Kate’s sister, and the always-impeccable Holland Taylor is right on target as their mother. Two poor choices in character design are saved by two superb choices in casting — Greg Kinnear somehow makes a dumb running joke about how his juice bar is nothing like the nationwide chain sound not all all whiny but somehow slightly mystified in a confident but sensitive way. And Will Forte as Kate’s ex elevates some sub-par dialogue about his perfect life. Other SNL-ers include Siobhan Fallon Hogan as the birthing instructor whose speech impediment just makes her sound even more inclusive and elemental and Fred Armisen as a stroller salesman. The wonderful Romany Malco is a highlight as Kate’s doorman. And I won’t spoil the surprise and give away the name of the star who shows up as Kate’s boss, who says things like “I am going to reward you with five minutes of uninterrupted eye contact.” I’ll just say he’s a great choice and does justice to that gray ponytail.

Fey is terrific; we’re on her side all the way. But it is worth seeing the movie a second time just to watch Poehler. As we first see her nervously dropping a little curtsy to the doorman on her way into Kate’s building, we understand that she is someone who may have had no education or opportunity but who has some sense of a bigger world than the one she has known. In one of her best scenes, she pretends to be Kate’s sister and we can see her mind working as she tries very hard to do what she thinks will be most supportive of Kate but also begins to get a different sense of her own capabilities and possibilities. Like Angie, this movie has some surprising depth and heart.