The WBA title bout took place at Madison Square Garden on June 16, 1983, which also happened to be Durán's 32nd birthday. The still inexperienced Moore (12–0) was game through the first three rounds, but by the 4th, Durán said he knew Moore couldn't hurt him, and an onslaught began. The pro-Durán crowd at ringside cheered as Durán relentlessly punished Moore. By the end of the sixth round, Moore's eye had swollen shut and he was floored near the end of the seventh. Finally the fight was stopped in the eighth round as Moore was taking such a horrific beating and Durán won his third world title. After the victory, Durán was hoisted up in the air as the crowd sang "Happy Birthday" to a sobbing Durán.
Durán later fought for the World Middleweight Championship, meeting Marvelous Marvin Hagler in Las Vegas on November 10, 1983. During the fight, Duran broke his hand and lost in a very competitive fight that went the full fifteen rounds. After 13 rounds, two of the judges had Durán one point ahead, and the other judge had it even. Hagler fought tenaciously to win the final two rounds and get a unanimous decision victory. The judges' scores were 144-142, 144-143, and 146-145. Despite the loss, Durán became the second man to take Hagler to a fifteen-round decision (Vito Antuofermo was the other) and the only one to do so while Hagler was the world champion.
Durán's 1983 fight with Davey Moore is referenced in the 2014 single, "The Possum," by American songwriter, Sun Kil Moon (i.e. Mark Kozelek), who often writes about boxers. Kozelek sings: "They threw hard vicious guttural B-flats that shook their opponent / Like a tough Roberto "Hands of Stone" Durán, in the seventh round / Davey Moore, June 16, 1983..."