You are mistaken. The House and the Senate both possess the power to imprison. This is well established and confirmed by the Supreme Court.
http://freerepublic.com/focus/news/3171794/posts?page=14#14
That power is quite limited as a practical matter. They can throw someone into the jail they have at the Capitol for a while for contempt, but they cannot prosecute someone of federal crimes. And Boehner has even ruled out that as an option, at least with regard to Lehrner...