Stu: So, uh, are you sure you're qualified to be taking care of that baby?
Alan: What are you talking about? I've found a baby before.
Stu: You found a baby before? Where?
Alan: Coffee Bean.
Zach Galifianakis pulled a similar Alan move in real life -- replace "baby" with "homeless lady" -- and you've got his date to the "Hangover 3" premiere ... who TMZ spoke to right before the big event!
Our photog spotted 87-year-old Elizabeth "Mimi" Haist on Monday in L.A. -- the woman Zach rescued from homelessness two years ago.
The story goes ... Zach became friends with Mimi at Fox Coin Laundry in Santa Monica back in 1994 -- where she would help people fold their clothes ... for tips.
When he found out she'd become homeless a few years ago, he decided to help out ... setting her up in a one bedroom apartment and paying her rent.
Zach also began taking Mimi as his date to his movie premieres -- and walked the red carpet with her at "Hangover 2," "The Campaign" ... and now "Hangover 3."
And how does Mimi feel about Zach? Check out the video ... it's adorable.