The duo picked up Best Male and Best Female Performances for their roles in 'Silver Linings Playbook' and later shared the gong for Best Kiss for the same movie.
Accepting the second award, Bradley said: ''Jennifer's not here but she was great to kiss.''
Adam Sandler and Chris Rock took to the stage to present Jamie Foxx and Samuel L. Jackson with the iconic golden popcorn statuettes for Best WTF Moment for 'Django Unchained', with Samuel stating ''If it wasn't for all of the fans we wouldn't have this golden popcorn.''
'Star Trek's Zoe Saldana, Zachary Quinto and Chris Pine were on hand to announce Marvel's 'Avengers Assemble' as winner of Best Fight which Tom Hiddleston, Joss Whedon, Chris Evans and Samuel accepted.
Samuel said: ''Thanks to all the fans but we all need to thank our fearless leader Joss Whedon,'' while Tom added: ''I'm happy to be hulk smashed any day of the week.''
Joss later took home the Movie of the Year for 'Avengers Assemble' and was introduced by Brad Pitt.
Tom also picked up the Best Villain award for his role as Loki in 'Thor' and paid tribute to One Direction singer Liam Payne's dog, who shares his name with the evil Marvel comic character.
He said: ''I would like to thank Liam Payne from One Direction, who I believe has named his dog Loki. Liam's dog is certainly better looking, better bred and most certainly more well known with more Twitter followers than me and even though they don't know who Liam's dog is in Asgard, it's all about getting the word out.''
Host Rebel Wilson won the Breakthrough Performance award for her role in 'Pitch Perfect' and shared the gong for Best Musical Performance with her 'Pitch Perfect' castmates.
Zac Efron, Danny McBride and Seth Rogen presented 'Twilight' actor Taylor Lautner with the Best Shirtless Performance award and he joked getting older had taken its toll on his impressive physique and added: ''For all of us shirtless actors this is like winning an Oscar. For all of us who do take our shirts of McConaughey, Tatum, Lena Dunham, this is it.''
Kerry Washington gave a glowing speech about her frequent co-star Jamie Foxx before he took to the stage to accept the MTV Generation award, his second gong of the night.
Macklemore and Ryan Lewis and Selena Gomez were among the performers at the ceremony.
It was announced at the end of the show that Rebel will also host the MTV EMAs in Amsterdam on November 10.
The MTV Movie Awards will air on April 15 on MTV UK, Sky 126 and Virgin 311.
MTV Movie Awards 2013 Winners List
Best Female Performance
Jennifer Lawrence 'Silver Linings Playbook'
Best Male Performance
Bradley Cooper 'Silver Linings Playbook'
Bradley Cooper and Jennifer Lawrence 'Silver Linings Playbook'
Tom Hiddleston 'Thor'
Rebel Wilson 'Pitch Perfect'
Best Shirtless Performance
Taylor Lautner 'Twilight Saga: Breaking Dawn Part 2'
Best WTF Moment
Jamie Foxx and Samuel L. Jackson 'Django Unchained'
Marvel's 'Avengers Assemble'
Best Musical Performance
Movie of the Year
Marvel's 'Avengers Assemble'
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