The comedy series and the British period drama both took home four accolades from the prestigious ceremony at the Nokia Theatre in Los Angeles, while 'Mad Men' and 'Mildred Pierce' were also awarded some of the top prizes.
'Modern Family' was named Best Comedy Series, with its stars Julie Bowen and Ty Burrell taking home the prizes for Best Supporting Actress in a Comedy Series and Best Supporting Actor in a Comedy Series respectively. Steven Levitan and Jeffrey Richman also won in the Writing, Comedy Series category.
Downton Abbey's gongs included Best Miniseries and Best Supporting Actress in a Miniseries or Movie for Dame Maggie Smith.
The show's writer Julian Fellowes was honoured for Outstanding Writing in a Miniseries, Movie or Dramatic special.
Accepting his statuette, Julian said: "When we were in the hotel a bit earlier, my wife said to me, 'I think we should just relax and enjoy the evening, because I don't think we're going to win.' Well, we're going to enjoy the evening now!
"And at the risk of sounding grandiloquent, I would like to thank you, the American industry. Ten years ago you kick-started my second career with an Oscar, tonight you have nurtured it, I am very grateful, thank you."
'Mad Men', an advertising drama set in the 1950s, was named Best Drama Series, while Kate Winslet and Guy Pearce both won for their roles in 'Mildred Pierce'.
Kate – who was named Best Actress in a Miniseries or Movie – said of her prize: "It doesn't matter how old you are or what you do in your life, you never stop needing your mum and I will never stop needing mine, so thanks mum, thank you so much."
Other winners included Julianna Margulies, who was named Best Actress in a Drama Series for her role in 'The Good Wife', while 'Friday Night Lights' star Kyle Chandler won Best Actor in a Drama Series at the ceremony which was hosted by 'Glee' star Jane Lynch.
63rd Primetime Emmy Awards full list of winners:
Drama Series: 'Mad Men'
Actress, Drama Series: Julianna Margulies - 'The Good Wife'
Actor, Drama Series: Kyle Chandler – 'Friday Night Lights'
Supporting Actor, Drama Series: Peter Dinklage – 'Game of Thrones'
Supporting Actress, Drama Series: Margo Martindale – 'Justified'
Writing, Drama Series: Jason Katims – 'Friday Night Lights'
Directing, Drama Series: Martin Scorsese – 'Boardwalk Empire'
Comedy Series: 'Modern Family'
Actor, Comedy Series: Jim Parsons – 'The Big Bang Theory'
Actress, Comedy Series: Melissa McCarthy – 'Mike & Molly'
Supporting Actress, Comedy Series: Julie Bowen – 'Modern Family'
Supporting Actor, Comedy Series: Ty Burrell – 'Modern Family'
Writing, Comedy Series: Steven Levitan and Jeffrey Richman – 'Modern Family'
Directing, Comedy Series: Michael Spiller – 'Modern Family'
Miniseries or Movie: 'Downton Abbey'
Actress, Miniseries or Movie: Kate Winslet – 'Mildred Pierce'
Actor, Miniseries or Movie: Barry Pepper - 'The Kennedys'
Supporting Actress, Miniseries or Movie: Maggie Smith – 'Downton Abbey'
Supporting Actor, Miniseries or Movie: Guy Pearce – 'Mildred Pierce'
Directing, Miniseries, Movie or Dramatic Special: Brian Percival – 'Downton Abbey'
Writing, Miniseries, Movie or Dramatic Special: Julian Fellowes – 'Downton Abbey'
Reality-Competition Programme: 'The Amazing Race'
Variety, Music or Comedy Series: 'The Daily Show With Jon Stewart'
Directing, Variety, Music or Comedy Series: Don Roy King – 'Saturday Night Live'
Writing, Variety, Music or Comedy Series: 'The Daily Show With Jon Stewart'