I had the same problem and here’s the solution that worked for me:
Go to Settings > Share Buttons > After Post Content and click Save changes. (You don’t actually need to change any setting.)
Well, here’s the bug: http://core.trac.wordpress.org/ticket/13471
It has been known for a month and not fixed yet.
Actually, it doesn’t simply work with with even <?php wp_link_pages(); ?>
When I click on the 2nd page link, it displays the first page.
