The 1980 Olympic Team USA defeats the USSR Red Army. "Do you believe in miracles? YESSSSSSSSSSS!" I was outside that arena and we were all singing God Bless America and nobody even cared that we would not win the gold til we beat the Finns in the next round (which we did).
Equally good: The 1976 Canada Cup in which Canada had to win three times before it counted. The neighbours called 911 because they thought my roommate and I were being killed.
Finally, the Game 7 between the Colorado Avalanche (I think) and the Florida Panthers, which went into triple overtime. If only the Panthers had scored, I would have made $48,000.
That was 1996 but it was a 4 game sweep for the Avs over Florida. The last game (game 4) was 3 OTs.