Go to Gmail at Settings > Accounts and import > Send mail as. Choose a name to send the mail, and your mail address. Click next and use the following configuration:
SMTP server: outlook-au.office365.com
Username: my-student-id@student.uts.edu.au
Password: your-uts-stuff-password
(And port 587, TLS connection).
You may need to try more than once as sometimes the server timeouts (it has a 9.99s timeout).
You'll receive an email in your UTS email account with a link to click to enable this feature.
The config is slightly different for staff than for students. This process worked for me in FastMail: http://darlinglab.org/tutorials/uts_networking/