I was wrong, the game does not end when the winning run scores. Here is the Ventura Wiki explanation:
The third point above led to Robin Ventura's "Grand Slam Single" in the 1999 NLCS. In the bottom of the 15th inning, the New York Mets tied the score against the Atlanta Braves at 3–3. Ventura came to bat with the bases loaded, and hit a game winning grand slam to deep right. Roger Cedeño scored from third and John Olerud appeared to score from second, but Todd Pratt, on first base when Ventura hit the home run, went to second, then turned around and hugged Ventura, as the rest of the team piled onto the field. The official ruling was that because Ventura never advanced past first base, it was not a home run but a single, and thus only Cedeño's run counted, making the official final score 4–3.
Theoretically, our runners could have all scored today but they stopped running and the ball was declared dead at some point. I think I saw the ball hit the wall and bounce back into play. Not sure if it bounced over the wall what the scoring would be......