The film stars Mickey Rourke as a wrestler forced into retirement - who tries to get on with his life by sparking up a romance and trying to reconnect with his estranged daughter - but who finds it tough to give up the ring.
Director Wim Wenders, who headed the Venice jury, praised Rourke's work, with an allusion to the heart condition his character suffers in the film, saying it was "a truly heartbreaking performance, in the very sense of the word."
Aronofsky dedicated the award "to all the wrestlers who we met along the way, who are working for 200 bucks a night who just want to entertain and are willing to sacrifice their bodies and their souls for it."
The Silver Bear for best director went to Russia's Aleksey German Jr for Paper Soldier (Bumaznyj soldat).
The acting prizes went to France's Dominique Blanc for her role as a jealousy-struck woman in The Other One (L'Autre) and Italian Silvio Orlando for his role in Giovanna's Father (Il Papa Di Giovanna), which charts a father and daughter's difficult relationship.
A special Lion award was given to German filmmaker Werner Schroeter, whose This Night (Nuit De Chien), about people fleeing a dictatorship, screened at the festival. The jury praised his " uncompromising and relentlessly innovative work over a period of 40 years".
The award for best young actress went to Jennifer Lawrence for The Burning Plain by Guillermo Arriaga.
Haile Gerima won a special jury prize and the screenwriting prize for for Teza - about the return of African intellectual Anberber to his native land, while it was under a harsh Marxist regime.
The debut film award was given to Pranzo Di Ferragosto by Gianni Di Gregorio.