The three-time Oscar-winning actress won for her performance as The Rabbi, Hannah Pitt, Ethel Rosenberg and The Angel Australia in the HBO miniseries "Angels in America."
Streep's award continued a winning night for the miniseries and for HBO.
"Angels in America" had already won acting awards for Al Paciono, Mary-Louise Parker and Jeffrey Wright, a directing award for Mike Nichols and a writing award for Tony Kushner, for his adaptation of his Pulitzer Prize-winning play.
HBO series "The Sopranos" (drama series writing), "Driftwood" (drama series directing) and "Sex in the City" (comedy series lead actress and supporting actress) won Emmys earlier in the evening.
Celebrity Families of 2014 [PHOTOS]