The 6-minute clip has gotten nearly 1 million views since it was posted on YouTube early Sunday.
"Thank you all for joining us today for this important discussion. It's in no way a publicity stunt. This is a serious, private conversation between three friends and 50 reporters with cameras," Baldwin as Trump said in the sketch.
"I flew here using the power of this hat," Chris Redd as West said before speaking in a stream-of-conscious manner about how he is a prisoner in another dimension and the 13th Amendment to the U.S. Constitution is a trap door.
As West continued to flit from topic to topic, Trump thought: "This guy can talk. He doesn't stop. He doesn't listen to anyone but himself. Who does he remind me of?"
"I really have a high IQ. I'm a stable genius. I got a big brain and I've got the best words," West continued.
"Oh, my God, he's black me!" Trump said.
Kenan Thompson, who played Brown and who looks astounded throughout most of West's rant, is heard in voiceover, thinking: "Oh, my lord! What have I gotten myself into? ... I've been on coalitions with Bill Cosby and O.J. Simpson and this is the first time I'm having regrets."
Baldwin has been playing the recurring role of Trump since 2016. This was his first appearance on the show this season.