Leto, a strong favourite, won the first trophy of the night for his role of a transgender AIDS patient in "Dallas Buyers Club".
"Frozen" defeated "The Croods", "Despicable Me 2", "Ernest & Celestine" and "The Wind Rises" to score in the animated category.
"Gravity" which has maximum nominations with "The American Hustle" won its first award of the night in the best visual effects category while the best costume design went to "The Great Gatsby".
Best animated short film Oscar went to "Mr Hublot" while "Helium" was named best live action short film.
"20 Feet from Stardom" was named the best documentary feature and best documentary short went to "The Lady in Number 6: Music Saved My Life".