Adele, Kelly Clarkson and Skrillex also picked up prizes during Sunday night's ceremony at the Staples Centre in Los Angeles.
The Black Keys took home a total of three awards - 'Best Rock Performance', 'Best Rock Song' and 'Best Rock Album' - while Dan Auerbach was also honoured in his own right in the 'Producer of the Year (Non-Classical)' category.
However, the group were beaten to the overall 'Album of the Year' prize by Mumford & Sons' Babel, which was presented by last year's winner Adele.
Prince made a surprise appearance to present Gotye and Kimbra with the 'Record of the Year' award for 'Somebody That I Used to Know', which also won 'Best Pop Duo/Group Performance'.
Gotye's longplayer Making Mirrors also triumphed in the 'Best Alternative Album' category.
fun. scooped a pair of general field awards, winning the gongs for 'Best New Artist' and 'Song of the Year'.
Although Frank Ocean ultimately lost out in the general field categories, he too won two awards.
In addition to the prize for 'Best Urban Contemporary Album', Ocean also shared the 'Best Rap/Sung Collaboration' accolade with Jay-Z, Kanye West and The-Dream for 'No Church in the Wild'.
Skrillex won both 'Best Dance Recording' and 'Best Dance/Electronica Album', while Adele won 'Best Pop Solo Performance' for 'Set Fire to the Rain'.
Kelly Clarkson triumphed in the 'Best Pop Album' category with Stronger, and Usher, Beyoncé, Carrie Underwood and Rihanna were also honoured.
The ceremony, which was hosted by LL Cool J, featured a collaboration between Sir Elton John and Ed Sheeran, while Maroon 5 duetted with Alicia Keys.
Rihanna, Damian Marley, Sting and Bruno Mars joined forces to honour Bob Marley, and John later returned to the stage to honour the late Levon Helm.
Other performers included Ocean, Underwood, Clarkson, Taylor Swift and Justin Timberlake.
4Music will air Grammys highlights in the UK tonight (Monday, February 11) at 10pm, repeated on Saturday, February 16.
Grammy Awards 2013 ceremony highlights - photo gallery: