The numbers mostly speak for themselves. Nope, I did not try to control for games where both teams allowed unearned runs.
Giants 2010 record in games when allowing any unearned runs
Regular season: 8-18
Overall: 9-21 (.300)
Giants 2010 record in games with opponent allowing any unearned runs
Regular season 27-6
Overall: 30-6 (.833)
In a Series as tight as this, the team that makes the fewest mistakes and which recovers most gracefully from their mistakes, is going to win.