How to Sync my Mail app with my Gmail account?
Check to see if Gmail on your Mac is set up to use IMAP instead of POP3 by going to Preferences > Accounts in Mail. IMAP syncs the read / unread status (among a host of other benefits).

If it's not set up to use IMAP then you'll have to remove the account and add it again, this time making sure to select IMAP in the account wizard.