And, of course, it had to be against the Giants...
"It's a fight, a blow-by-blow verbal battle."
- Vin Scully, June 30, 1959
Rich provides both the clip and a transcription.
Reading the transcript really makes clear what a remarkable piece of reportage this is, considering that Scully was doing the whole thing on the fly. Just keeping track of all the participants is something. And what participants! Willie Mays sets the whole thing off. Besides manager Walter Alston for the Dodgers there's Gil Hodges and Don Drysdale, and Don Zimmer, when he was still a stick-thin shortstop with cable-like veins in his neck rather than the chubby old gerbil who sat next to Joe Torre in the Yankee dugout.
The umpires look really bad here, because not only did they change their original call, they had to change it a second time when Alston (apparently) pointed out the correct, albeit bizarre) ground rule that changed a home run into a ground rule double. On the other hand, what's even more amazing is that no one was tossed from the game.
The umpires looked even worse later in the same season, when something similar happened in an even bigger spot. From the Wikipedia article on the Coliseum:
The Milwaukee Braves were playing the Dodgers in the Coliseum on September 15, 1959, and Joe Adcock hit a ball that cleared the screen but hit a steel girder behind it and got stuck in the mesh. According to the ground rules, this should have been a home run. However, the umpires ruled it a ground-rule double. Then the fans shook the screen, causing the ball to fall into the seats. The umpires changed the call to a homer, only to change their minds again and rule it a ground-rule double. Adcock was left stranded on second. The game was tied at the end of nine innings and the Dodgers won it in the tenth inning. At the end of the regular season, the Dodgers and Braves finished in a tie. The Dodgers won the ensuing playoff and went on to win the World Series. If Adcock's hit had been ruled a home run, the Braves may have won the game and could have gone on to win the pennant by one game.