Answer: you need to integrate an external email box with your CRM account. Here's how:
SETUP -> PERSONAL SETTINGS -> EMAIL SETTINGS
If you haven't configured your Zoho mail, click the big green Configure Now button. Then you'll be presented with this screen:
Click on +Add new Mailbox
Enter a Name for this Account in the Account Name, Enter the Email address (e.g. Joe@smith.com) in both the Email ID and User Name fields. You'll also need the Server Name, Port and whether or not the mail server uses SSL. Enter the Password, select the Delete settings, and Test the Account by clicking the Test Account Button. If the Test is successful, you'll move onto the SMTP configuration screen. You can use the Zoho SMTP or choose to configure a custom SMTP. Click Save.
Once you've added your account, close the screen which will take you back to the Zoho Mail Add-on screen. You'll now see the new mailbox as an option in the Send Mail As: Drop down. Choose that mailbox. Now all the mail you send from your CRM account will be From that address!
NOTE - if you prefer NOT to have the mail from the account you added pulled inside of your CRM account, you can choose the Zoho mailbox in the first drop down.