Two possibilities I can think of, off the top of my head.
The easy way (maybe) would be to change their current password to the new password upon completing the password change.
I'm not entirely sure that's possible, or how to do it, but it's one idea.
The other would be to change all your authentication code to allow for an old password variable, which you automatically delete after 24 hours (or however long you want it to be stored).
The problem is if the person is changing their password for a security reason, you don't want to support the old password. Plus you have to redo all your auth validating in your pages, so this probably isn't a good fix.
A third possibility doesn't really do what you want to do, as it just logs out the user upon completing the password change.
If you can't automatically update their current password without them having to do it themselves, you might just want to keep it the way it is.
If you need to redirect to another page to authorize, or something to that effect, you may want to have their original destination stored in a variable and then automatically redirect them to that page once they've entered their login info.
Hope that helps.
