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

Playoffs: 1-3

Overall: 9-21 (.300)

Giants 2010 record in games with opponent allowing any unearned runs

Regular season 27-6

Playoffs: 3-0

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.