LHP Andy Pettitte
I'm on record as not being an Eduardo Nunez enthusiast -- as I've said many times now, he's the only utility infielder who can't field. As a designated hitter, I'm not sure he's much better. Yes, he hit .360 against southpaws in a small sample this year, but a small sample is likely all it is. Last year, in twice as much playing time, he hit .277/.314/.429 against them, which might sound sort-of good except that the average AL right-hander hit .268/.338/.429 against lefties last year. The real "lefty-mashers" set a really high bar.
That said, with the long cold snap endured by Andruw Jones, the Yankees didn't have much choice. There is an interesting alternate scenario wherein the team looked at Jones and said, "He had 12 home runs in 161 at-bats at the end of July. Yes, he fell off a cliff at that point, but the real guy is still in there somewhere. We're only going to see one left-handed starter in this series, so let's gamble on the upside."
I'm not saying that answer is any better than the one they chose, but it's an equally legitimate answer.