It is a slight corruption of a Bible passage: "Neither do men pour new wine into old wineskins. If they do, the skins will burst, the wine will run out and the wineskins will be ruined. No, they pour new wine into new wineskins, and both are preserved." Matt. 9:17.
Note, these are wineskins, not bottles (hence, the modern corruption) in the passage. So, it's a play on the saying though, as you point out, it is a little off kilter.
I was thinking that “Put leftover wine in new bottles” would make some sense — for cheapo types, wanting to recycle party left overs.