ESPN has a terrific feature involving interviews with many of the participants in that game. From the article, here's Vin Scully's recollection ogf the moment Gibson hit the home run:
When he hit the home run, naturally, I let the crowd go bananas. I didn't say anything for over a minute, and then I said, 'In a year that has been so improbable, the impossible has happened.' I don't know where it came from. Sometimes I often think the inspiration comes from above. It was the most theatrical home run I had ever seen. You looked on stage and he wasn't there, and suddenly he appears on stage and the crowd erupts. He's limping, and then suddenly he hits the home run. The whole thing was theater. It was perfect theater.
Appropriately, Major League Baseball has the entire game in their classics on You Tube. You can watch it below.