Fight #47: Floyd Patterson vs. Ingemar Johansson 2, June 20, 1960, Polo Grounds, New York City.
The first rematch on the list. In the first fight, Patterson lost the world heavyweight championship when he was knocked down seven times in four rounds before the fight was waived off. In that fight, Patterson just could not get past Johansson's left jab, and it eventually became target practice for Johansson's Howitzer of a right hand. The first knockdown basically ended that fight, as Patterson stumbled around the ring in a daze after that, getting knocked down six more times.
The rematch went completely different. You can tell that Patterson was trained very well for this fight. Johansson's jab was not as crisp as in the first fight, and early on Patterson figured out how to time Johansson with left hooks, which landed with enough force that Johansson was obliged to keep his right hand tucked against his chin to protect himself, rather than to attack Patterson. After winning most if not all of the first four rounds, in the fifth Patterson landed a perfect leaping left hook that sent Johansson to the canvas. After Johansson got up, he landed the same punch again, knocking Johansson out. This made Patterson the first ever two-time heavyweight champion.
A couple interesting things about this fight: Cus D'Amato trained Patterson. Two decades later he would train Mike Tyson. You can definitely see the resemblance in their fighting styles, as Patterson also used a variation of the peek-a-boo style that Tyson perfected. The other thing is, back then the heavyweights were a lot smaller than they were today. Patterson weighed no more than 190 pounds for these two fights, and Johansson weighed 195. Today, they'd be in the cruiserweight division. I think a lot of times when people talk about the lack of athleticism in the heavyweight division they are really talking about how large heavyweights today are.
Here's a video of the fight: