All apparently went well, as Meyers - who got choked up a couple of times during the retelling - showed off pictures of his new son, who was quickly taken to the hospital after his dramatic entrance into the world.
And yet, there's another shocking element to the tale: Meyers called an Uber to take them to the hospital - but once his wife started physically giving birth as soon as she got into the lobby, they had to bail on that plan. And Uber still charged them for a canceled ride.
Meyers described the situation like so: When his wife started to have contractions, they realized they better get going to the hospital. "We get into the lobby of our building. I have called an Uber. The Uber is outside," Meyers explained. "And we basically get to the steps of our building, we're in the lobby and we're walking down the steps, and my wife just says, 'I can't get in the car. I'm going to have the baby right now; the baby is coming.'"
Later in the story, Meyers ticked off a list of people he wanted to thank: the doormen in their building, the police officers and firefighters who showed up to help, the doctors. Then he added a bleeped-out expletive directed at "the Uber driver who charged me."
The audience burst into laughter and started applauding. "I mean, for real," Meyers continued. "Because we did you a huge favor."
Granted, it's possible that the Uber driver didn't realize why the ride was canceled (Meyers was a bit preoccupied, after all) and the policy is to charge a cancellation fee if someone doesn't show up to their car.
And don't worry, the story has a happy ending - although a "Late Night" spokeswoman declined to elaborate on whether they got a refund, when we reached out to Uber on Tuesday morning, a spokesman sent us the following statement:
"We are so happy for Seth and Alexi on the birth of their second child. We've refunded the trip and send them our best wishes."
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)