Actor Jeffrey Tambor (2-R) and show creator Jill Soloway (C) holds the award for Best TV Series, Comedy or Musical for "Transparent," in the press room at the Golden Globe Awards on January 11, 2015 in Beverly Hills, California

Online retail giant Amazon scored its first ever Golden Globes on Sunday with two wins for dark comedy "Transparent"—a breakthrough in its bid to catch up with streaming pioneer Netflix.

The series, starring veteran actor Jeffrey Tambor, tells the story of a man who has transitioned to become a woman and is working out the thorny details of telling his family.

It took home prizes for best comedy/musical series and for Tambor.

"This is dedicated to too many trans people that died too young," said series creator Jill Soloway. "Maybe we'll be able to teach the world something about authenticity and truth and love."

A few minutes later, Tambor accepted his trophy, saying: "Oh, this is big. This is much bigger than me."

"I would like to dedicate my performance and this award to the transgender community," he added.

In October, Amazon ordered a second season of the series—the creation of Soloway, an Emmy-nominated writer on cult series "Six Feet Under." The first season was released on September 26.

Amazon has recently bolstered its streaming video offerings.

But so far, its own original content has not quite reached the popularity level achieved by Netflix, with its signature series "House of Cards" and "Orange Is The New Black."

"House of Cards" star Kevin Spacey took home the prize for best actor in a television drama—his first Globe in eight nominations.

"This is just the beginning of my ," Spacey joked in the Southern drawl of his character, Frank Underwood.

Actor Jeffrey Tambor holds the award for Best Actor - TV Series, Comedy or Musical for his role in "Transparent," in the press room at the Golden Globe Awards on January 11, 2015 at the Beverly Hilton Hotel in Beverly Hills, California

Showtime's new series "The Affair"—the story of a love affair gone wrong, told from the perspective of both the man and the woman—took home honors for best drama and best actress (Ruth Wilson).

The best drama category had been seen as a tough one, with "Downton Abbey," "Game of Thrones," "The Good Wife" and "House of Cards" also in the mix.

Another big winner on the television side was "Fargo"—a miniseries based on the Oscar-winning crime thriller film by Joel and Ethan Coen.

It took home prizes for best miniseries or television movie, and best actor in a miniseries or TV movie for Billy Bob Thornton—besting HBO's widely acclaimed "True Detective" in both categories.

Gina Rodriguez took the Globe for best comedy TV actress for her breakout performance in "Jane the Virgin"—based on a Venezuelan telenovela.

"Thank you to my mom and my dad for telling me to dream big and to never stop dreaming," Rodriguez said.