Rocky III begins with the ending of the 15th round of the rematch between Rocky and Apollo Creed, with Rocky Balboa becoming the new heavyweight champion of the world. This is followed by an opening montage of scenes that explain what happened in the time between Rocky II and Rocky III. In the five years since winning the heavyweight title from Apollo (1976-1981), Rocky has a string of 10 successful title defenses. As his winning streak grows, so does his fame, wealth and celebrity, and soon Rocky is seen everywhere, from magazine covers to TV show guest star appearances. Rocky is also heavily merchandised, sponsoring varied products and services. At the same time, a ferocious new boxer named James "Clubber" Lang (Mr. T) is climbing the ranks, rapidly becoming the number one contender for Rocky's title.

Rocky’s brother-in-law Paulie (Burt Young) has grown jealous of Rocky’s accomplishments. After a night of heavy drinking, Paulie stumbles into a video arcade, hurls an empty whiskey bottle through a ROCKY pinball machine in a rage and is arrested. Rocky bails him out of jail and, on the way to Rocky's car to ride home, Paulie begins berating Rocky for forgetting him on his climb to the top. Paulie swallows his pride and asks Rocky for a job, which Rocky grants him.

Rocky agrees to a charity match with wrestling champion Thunderlips (Hulk Hogan). While Rocky treats the match as a light-hearted exhibition, Thunderlips seems to be taking it seriously, body-slamming Rocky and throwing him out of the ring. Rocky shouts to Paulie (his new ringman) "Cut my gloves off!" The gloves come off and Rocky fights back, even managing to throw Thunderlips out of the ring himself. Just as the match is about to degenerate into a type of shoot fight, the bell rings and the match is declared a draw. Thunderlips calms down, and it's clear that his aggression earlier was just for show. (Rocky: "Why'd you get so crazy on me out there?" Thunderlips: "That's the name of the game.") A now smiling Thunderlips has his picture taken with Rocky's wife and kid.

Rocky has a statue unveiled in Philadelphia and reveals his plans to retire from boxing. The crowd of Rocky fans disapprove of his decision. Clubber Lang, who is in attendance at the ceremony, publicly challenges Rocky, this time criticizing Rocky’s title defenses as being intentional set-ups against weak, over-matched "bums." Lang also berates the politics of boxing, the reason Lang feels he hasn't been awarded a title shot. Furthermore, he harasses Adrian. Angered by a sexually suggestive remark Lang makes towards Adrian, Rocky agrees to the fight, but Mickey, his trainer, wants no part of it. Returning home, Rocky argues with Mickey; Mickey admits to Rocky that the fighters he defended his title against were good fighters but "hand-picked", only because Rocky received such a bad beating in his win over Creed that Mickey took it upon himself to make sure Rocky remained successful and healthy. He also tells Rocky that Lang is a young, hungry "wrecking machine" and that Rocky has no chance of beating him, as he hasn't retained his edge as a fighter. Rocky manages to convince Mickey to train him regardless, but his Las Vegas-style training camp is filled with distractions and Rocky clearly does not take the challenge seriously (similar to Creed in Rocky I). Clubber's relentless training regimen of working out by himself in a derelict building with whatever objects he has and running through city alleys clearly shows that he is taking his preparation for the bout far more seriously.

Lang and Rocky meet at Philadelphia's Spectrum. During a melee before the fight, Mickey is shoved out of the way by Lang and suffers a heart attack. A now distraught Rocky wants to call the fight off, but Mickey angrily urges him on while he stays in the dressing room. By the time of the fight, Rocky is both enraged and severely distracted by his mentor's condition. The fight begins: Rocky starts by pounding Lang with several huge blows, going for an early knockout, but the stronger and better-prepared Lang is unfazed and quickly takes charge, dominating Rocky and knocking him out in the second round. Beaten, Rocky makes his way back to the dressing room and to the dying Mickey. Kneeling at his side, Rocky speaks to his friend, telling him that the fight ended in the second by a knockout, which Mickey misinterprets as a win for Rocky, as he passes away. Following the funeral, Rocky faces a depression mixed with anger and hopelessness.

Stopping by Mickey's closed gym, Rocky is confronted by Apollo Creed, who offers to help train him. Previously, Creed had been insulted to his face by Lang, who mocked Creed as a "has-been" and refused to shake his hand. Apollo makes a pitch to snap Rocky out of his funk and get him back on the winning track. He vows to train Rocky to fight Lang again, the way Apollo thinks he should be fought. He slowly convinces him that he can regain the fire Rocky thrived on in his earlier days, and tells him he must again have the "eye of the tiger", his fighting spirit, mainly by starting from scratch. Apollo takes Rocky to the slums of Los Angeles so that Rocky can get back to basics. The duo also meet up with Creed's old manager, Tony "Duke" Evers, who has enthusiastically agreed to assist Creed in training Rocky. At first, Rocky is too demoralized to put forth his best efforts, which repeatedly frustrates Apollo. However, after admitting to Adrian that he's afraid, that his previous post-Apollo fights were set-ups and that he feels responsible for Mickey's death, she tells Rocky he has no right to feel guilty over Mickey, who was a grown man and made his own choices. She also tells him to fight for himself and no one else. Rocky is then able to pull himself together to train as hard as he can, adding some of Apollo's speed and skill to his own style of fighting. During his training, Rocky forges a deep bond with both Duke and (especially) Apollo, their relationship evolving from former adversaries to close friends.

The rematch is held at Madison Square Garden in New York City. At the start of the fight, Rocky sprints from his corner, fighting with a level of skill and spirit that no one, including Lang, expected. As a result Rocky completely dominates the first round, demonstrating his new-found speed. After the bell, Clubber, who is in a fit of rage over what has just happened, has to be restrained by his trainers. In the second round, Lang gains the upper hand, and Rocky adopts an entirely different strategy that bewilders Apollo; he intentionally takes a beating from Lang, whilst taunting him for being unable to knock him out.

In Round 3, Lang, who is used to winning fights swiftly with knockouts in the early rounds, becomes increasingly angry and quickly exhausts his energy trying to finish Rocky off with repeated knockout blows, most of which miss the newly-agile Rocky entirely. Rocky taunts Lang in order to psyche him out, with taunts such as, "My mother can hit harder than that'", and, "You're not so bad, you're not so bad, you're nothing". The quick-tempered Clubber is infuriated. He attacks even harder, walking right into Balboa's trap. The tide turns, and Rocky is able to overpower the winded and outfoxed Lang, landing blow after blow and dodging Lang's attempted punches before knocking him out.

Soon afterwards, Rocky and Apollo return to Mickey's gym, with Apollo revealing the price of his training: a third fight with Rocky. However, this time it would only be a sparring match between two new friends, which Rocky accepts.