Place this file in Magento installation root folder. Then change the database details & run the script. Last, change the database prefix in app/etc/local.xml.

mag_change_db_prefix.php

<?php
//Add Database details
$database_host = "localhost";// DB Host
$database_user = "dbuser"; // DB User Name
$database_password = "dbpassword"; // DB Password
$magento_database = "dbname"; //DB Name
$table_prefix = "dbprefix_"; // DB Prefix

//Do the action
$db = mysql_connect($database_host, $database_user, $database_password);
mysql_select_db($magento_database);
$query = "SHOW TABLES";
$result = mysql_query($query) or die('Err');
while($row = mysql_fetch_array($result)) {
    $old_table = $row[0];
    if(preg_match('/'.$table_prefix.'/', $old_table)) {
        echo "Table $old_table already done<br/>\n";
        continue;
    }

    $new_table = $table_prefix.$old_table;
    echo "Renaming $old_table to $new_table<br/>\n";
    $query = "RENAME TABLE `$old_table`  TO `$new_table`";
    mysql_query($query);
}
?>