How do I perform maintenance on a master DNS/DHCP (BIND9/ISC-DHCP) Ubuntu server?

I'm running non-GUI Ubuntu Server 12.04.2 LTS (64-bit) on my 2 DNS/DHCP servers.

Both servers are running BIND9 9.8.1-P1 and ISC-DHCP-SERVER 4.1.ESV-R4-0ubuntu5.6. Please note that for DNS I'm running them in a master/slave configuration, and for DHCP they are running a failover configuration.

Ideally, I'd like to perform maintenance on the master/primary first, and once it's back up and running, I'd like to then take care of the secondary/slave. Maintenance will consist of installing various updates and performing a restart.

I'm uncertain how to gracefully bring each machine down without losing/interrupting service. Any advice is greatly appreciated!