Bubic, 28, has been on the 60-day injured list since mid-May for elbow and shoulder soreness. He has a 4.11 ERA through nine starts this season, a year removed from tossing a stellar 2.55 ERA in 20 starts.
Duran, 25, has a 3.38 ERA through 37 games with 61 strikeouts in 42.2 innings at the Triple-A level this season.
This now marks the second pitcher the Dodgers have traded for at the deadline, with the first being superstar Tarik Skubal (details here).
Other pieces the Dodgers added at the end of the deadline include catcher Hunter Feduccia and relief pitcher Jacob Kmatz in a deal with the Tampa Bay Rays that sent outfielder Jack Suwinski and international bonus pool money.