301 Redirect from one url to another url (in different domain) transfer the ranking in Google?

[positivethinking]

Hello, I found very serious issue on my web site caused by Hosting comp.
For example,

mysite.com/page1 is my site and it's original page.

I found the hosting company generate url for the same page such as
mysite.webserverID.hostingcompdomain.com/page1

Somehow mysite.webserverID.hostingcompdomain.com/page1 is ranked in google top 4 for the keyword.
There are hundreds of pages like that. I feel all my SEO effort are waisted.

If I do 301 redirect from
mysite.webserverID.hostingcompdomain.com/page1 to
mysite.com/page1,

does mysite.com/page1 page rank in the top 4 for the keyword?

Any comment will help.
Thank you,