I can attest to this.
One night I woke up with a rat in my room. After thinking about what to do in a cold sweet hiding under my covers for about 2 minutes I realised I should probably just get one of our cats to sort it out.
First cat I found was Bella who we had got from a pet store several years ago, I took her to my room and watched to see how she reacted. She smelt the rat and went closer to investigate. She found where it was hiding she pretty much chased it and clawed at it. I gave her a few minutes but she did a pretty pathetic job and eradicating it.
By this time Dante a cat who came to use after being abandon by its owner and surviving on its own few several weeks had been woken up and came to see what the fuss was. He pretty much took one pounce at it grabbing it around the neck. Problem solved.