Star Wars: The Empire Strikes Back won an Academy Award for Best Sound and a Special Achievement Award for Visual Effects.
George Lucas' second installment had been nominated in four categories at the 53rd Academy Awards ceremony.
The Empire Strikes Back was also nominated for Best Original Score and Best Production Design but didn't win in those categories.
Bill Varney, Peter Sutton, Steve Maslow and Gregg Landaker collected the Oscar for Sound for The Empire Strikes Back.
Billy Dee Williams, who played Lando Calrissian in the Original Trilogy, presented the award alongside Bernadette Peters.
Johnson, Richard Edlund, Denis Muren and Bruce Nicholson went up on stage to receive the Special Award.
Follow The Star Wars Underworld on Twitter @TheSWU for more updates about this story and other breaking Star Wars news.