Login to your router and enable SSH. You will find the SSH related settings at [http(s):// System (Tab).
You should see something similar to the screenshot below:
Apply at the bottom of the page after you enable SSH.
Login to you root through a terminal:
$ ssh -l admin 192.168.1.1 firstname.lastname@example.org's password: admin@(none):/tmp/home/root#
Issue the below command to reset the DNS Cache.
admin@(none):/tmp/home/root# killall -1 dnsmasq
Your router cache should be reset now. Alternatively, you can reboot the router to reset the cache.