"I found this photo in the AP archives yesterday and wrote about the differences from 1949 and today on the Photography blog here . It's hard to believe that this shot was made as Tommy Henrich approached home plate after hitting a walk-off home run to win the first game of the '49 series 1-0. A World Series game! For some reason all the excessive exuberance shown today by players after every little thing bothers me. Seeing this old photo just made me smile."
The whole team did not go out to mob Henrich, as you can clearly see in the photo. See No jube at the plate? Archival photo shows walk-off home run in 1949 World Series. (Hat Tip: David Pinto's Baseball Musings)
I guess it depends on what you call old school (David Pinto's blog entry on this was titled "Old School Walk-Off"). This link shows Mazeroski’s series winning HR in 1960. I know it is different because it ended the series where as this one from 1949 was just the first game. But it looks like alot of the team came out to home plate to congratulate him as fans poured onto the field.
Then there is Bobby Thomson’s series winning HR in the 1951 NL pennant playoff
Again, it is a little different since it won a pennant.
But here is Dusty Rhode’s HR to win game 1 in the 1954 World Series. The whole team comes out to congratulate him at home plate and you also see Willie Mays jumping up and down as he rounds the bases. It is about 10 minutes long and the HR comes at the end, of course.
Here is a video that shows Eddie Mathews hitting a walkoff HR in game 4 in the 1957 World Series. It looks like a big celebration at home plate
So sometimes in the old days they had big celebrations after walk-off HRs.