I believe there is a module called Login toboggan which will allow you to do exactly what you want.
From the module page:
The LoginToboggan module offers several modifications of the Drupal
login system in an external module by offering the following features
and usability improvements:
Allow users to login using either their username OR their e-mail
Allow users to login immediately.
Provide a login form on Access Denied pages for non-logged-in
The other brings the user to a separate page, but returns the user to
their original page upon login.
Optionally redirect the user to a specific page when using the
'immediate login' feature.
Optionally redirect the user to a specific page upon validation of
their e-mail address.
Optionally display a user message indicating a successful login. ...
I believe when someone request a password, the format of the link will be similar to this one:
If so, you can create a rule to redirect the user upon login to a specific page. However, add one condition which will be:
Data comparison: the link should not contain the word reset
Hope it helps,