How to move Contextual Links?
you can create multiple tpl.php files for blocks based on the specific block, the module that created the block.


  Clone block.tpl.php to "block--block--[block-id].tpl.php" file


after try code, I don't' encourage you to do this, but it maybe the solution for you:

&lt;section id="&lt;?php print $block_html_id; ?&gt;" class="&lt;?php print $classes; ?&gt; clearfix"&lt;?php print $attributes; ?&gt;&gt;
    &lt;div class="block-content"&gt;
      &lt;?php print render($title_prefix); ?&gt;
      &lt;?php print render($title_suffix); ?&gt;
      &lt;?php if ($title): ?&gt;
        &lt;h2&lt;?php print $title_attributes; ?&gt;&gt;&lt;?php print $title; ?&gt;&lt;/h2&gt;
      &lt;?php endif;?&gt;
      &lt;?php print $content ?&gt;
    &lt;/div&gt;
&lt;/section&gt;


=> Clear cache