Amazon seems to be having little trouble getting Alexa into people's homes.

The giant e-tailer said on Tuesday it had sold "tens of millions of Alexa-enabled devices" around the world during the holiday season, making it the voice-activated digital assistant's best yet. The Echo Dot, a hockey-puck-shaped smart speaker, was the best-selling Amazon device during the holiday season and "the best-selling product from any manufacturer in any category across all of Amazon," the e-tailer said.

Amazon, which said this year marked its "biggest holiday season," also reported sharp growth in its services. More than four million people started free Prime trials or bought memberships to the two-day shipping service in one week alone, the company said.

The growth of Alexa devices buttresses Amazon's lead in the smart speaker market, where Google and Apple both want to make their mark. In addition to Amazon products, Alexa is being built into a host of other products, including cars, phones and DVRs.

As is typical, Amazon's press release was light on hard numbers. Still, the holiday season appeared to be merry for Amazon, with small businesses and entrepreneurs receiving orders for "more than one billion items," a record.

The company also listed its Amazon Music holiday earworms, reporting "Christmas" by Michael Bublé was the most played album during the season and "All I want for Christmas is You" by Mariah Carey was the most streamed holiday song.