When you say that the game went down to the wire, what you mean is, it was not possible to predict the outcome till the very end. When something goes down to the wire, it is full of suspense.
Example: The two teams are good. I have a feeling that the game will go down to the wire.
The expression is usually used to mean `at the very last minute’ or `at the very end’.
Example: ”Remember the assignment that I had to submit last week? I really went down to the wire on that one.”
( which means that you submitted it at the very last minute).
The expression come from the world of horse racing. In the old days, it was common practice to stretch a metal wire across the finishing line and the first horse that crossed the wire was declared the winner. So when you say `down to the wire’, what you actually mean is `up to the finishing line’. In other words, the race was exciting right up to the finishing line.