The odds of seeing this moment are wild ... to have Mike be called up from the minors this year AND to have S.F.'s schedule put the team in Boston this season are incredible coincidences.

But, the two squads took advantage of the opportunity -- allowing 80-year-old Carl to hurl the first pitch to 29-year-old Mike before the Giants played the Sox in the 2nd game of their 3-game series.

The video of the interaction is spine-tingling ... Mike has a huge smile on his face the whole time, and Carl -- one of Boston's all-time greatest athletes -- is clearly loving the moment too.

The Yastzemski's shared an embrace in the middle of the diamond after throw ... and when the game ended, Mike called it all "special."

"Honestly, I was thinking about the last time we had played catch," Mike said. "I remembered a time probably during Thanksgiving when I must have been 7 or 8 at his house."

"Being able to relive that and to go through that again on this type of scale and to have such a warm welcome from everyone was really awesome."

Mike killed it in his debut in the same batter's box Carl used to play in ... so far in the series, he's 3-for-11 with a home run, 4 runs scored and 2 RBIs. His team's gotten both wins too!