Found a solution from this thread: http://wordpress.org/support/topic/upgrade-to-34?replies=10
If you are getting the yoursite.com/wp-admin/upgrade.php?_wp_http_referer=%2Fwp-admin%2F error, this worked for me: Navigate via FTP to your installation. Check to see if the upgrade.php file is there. If not, download WordPress 3.4.2 from http://www.wordpress.org. Unzip the download and navigate to the wp-admin folder. Locate the upgrade.php file and FTP it to your installation. Somehow the in-app update process download was corrupted and missed the required upgrade.php which the redirect points to after the update. Good luck!
Looks like for me, the upgrade.php file was missing from wp-admin folder. Downloaded 3.5.2 from wordpress.org, then FTP'd upgrade.php. It then prompted for a database upgrade, and I'm back in action.
Thanks to chowsir for the fix, and Krishna for quick response.