Tommy Hunter, who started instead of Lee, lasted only four innings.
"I'm not sure how many runs he was going to score off Bumgarner," Texas General Manager Jon Daniels said of Lee.
The Rangers would need to extend the Series to seven games to win, but now Lee is not an option to start Game 7. He would have been had Texas arranged its World Series rotation with three starters.
Dropping Hunter, who failed to pitch beyond four innings in all three of his postseason starts, would have required Lee to start twice on short rest and C.J. Wilson and Colby Lewis to start once on short rest.
Lee has started 228 games, never on short rest.
"We talked about it, pros and cons," Daniels said. "The first time we talked about it was before the postseason began, really, and I think we decided if we could avoid it, we'd like to.
"It's not just one start. It's the starts after that. Other guys may have to pitch on three days' rest. You may be taking a start away from a guy that you wanted to pitch.
"So we decided, unless a certain circumstance came about, we were probably going to try to avoid it. I'm glad we did."
Lee is on the verge of a huge payday in free agency. The New York Yankees— and their bottomless sacks of money — have targeted Lee, but so have the Rangers.
"We've made it clear we'd like to have him back," Daniels said. "I know we're not the only club that would like to have him.
"It's a competitive market, as it should be, and we'll see what happens."
The Rangers will throw money at Lee in an effort to retain him, but they have a more challenging decision on designated hitter Vladimir Guerrero.
The Rangers paid Guerrero $5.5 million in base salary this season. He and the Rangers have a mutual option at $9 million for next season.
Guerrero, 35, batted .300 with 29 home runs. His numbers dropped from the first half, when he hit. 319 with 20 home runs.
He has batted .236 in postseason play, with no home runs, two walks and 15 strikeouts in 55 at-bats.
In the Series, he has one hit — a single — with four strikeouts in 10 at-bats.
"He's got a pretty big body of work that we can evaluate," Daniels said.
"For me, he's clearly a first-ballot Hall of Famer. … We're not going to evaluate him on the two weeks of games when he's had … a career of excellent performance."