The resistor limits the current throughout the entire wire. Think of it as a pipe filled with marbles, you stand at the beginning of the pipe and add marbles and I am at the end of the pipe and I use my hand to make it difficult for you to push the marbles in. Even though I am at the end of the pipe resisting the flow of marbles, the marbles at the beginning of the pipe are also resisted.
Current does not only slow down at the resistor. The entire series line the resistor is placed in has reduced current due to resistor.