The World Cup winners went ahead through Thomas Muller in the 18th minute but were pegged back by an Ikechi Anya strike in the second half. However, Muller netted again to earn his side a hard-fought three points.
"I am happy with the three points, that was my main expectations of the players," Low told Sky Sports News.
"I knew it would be difficult. Scotland had not lost in a year. The first half we controlled, we pressed them back, we didn't give them many chances and we managed to get a lot of chances ourselves.
"We lost a little bit of control of the game in the second-half, Scotland scored but we reacted well and came back and scored. So, as I say, I am happy with the three points."
Germany are next in qualifying action against Poland on October 11.