Web Server Can't Connect to Database Server

I have a web server (Ubuntu 14.04 LTS) and a database server (Ubuntu 12.04 LTS). UFW is enabled on both. The web server allows all outgoing traffic. The database server only allows incoming requests on 3306 for the private IP address of the web server. I've also tried disabling UFW on both servers, but the following results are the same.

I'm unable to connect to MySQL from the web server. It hangs on SYN_SENT (using tcptrack) and fails after a short time.

I'm trying to connect using mysql -u <username> -h <database-private-ip> -D <database-name> -p</database-name></database-private-ip></username> from the web server.

It fails with the error ERROR 2003 (HY000): Can't connect to MySQL server on '<database-private-ip>' (110)</database-private-ip>

I'm able to connect to mysql from the database server with the same credentials (as expected). The bind-address in my.cnf is set to 0.0.0.0. And I can ssh from the web server to the database server.

Can anyone offer some guidance on how to get these two communicating successfully?