The show depicted a 6-year-old asking her family's new Amazon Echo "can you play doll house with me and get me a doll house?"
The device followed the command, ordering a KidKraft Sparkle Mansion Dollhouse, in addition to "four pounds of sugar cookies".
The parents realised what had happened and have since added a code for purchases. They have also donated the dolls' house to a local children's hospital.
However, viewers' Alexa gadgets also complied with the request and also bought dolls' houses.
Voice-command purchasing is a default option on the Echo. Experts said the incident highlighted the need for people to password protect their Amazon Echos.
David Emm, a security expert at Kaspersky Labs, a web security firm, said: "People need to find a compromise where they feel comfortable between achieving security and enjoying the convenience of these gadgets. It is certainly advisable to opt for having a verbal password or code to minimise the risk."
He added that a growing wave of cyber criminals are targeting smart devices to hack into people's accounts.
Amazon did not respond to a request for a comment.