You can enable ssh server on ESXi and copy your ssh key to the server, read the following on how to do that: Monitor LSI 3ware raid controller on ESXi
Then to shutdown the virtual machines and power off the ESXi server I would schedule a cronjob on a remote physical server:
20 9 12 22 * root ssh 10.1.1.140 /sbin/shutdown.sh
30 9 12 22 * root ssh 10.1.1.140 /sbin/poweroff
In this case shutdown the virtual machines at Dec. 22, 9:20 AM and power down the ESXi server at Dec. 22, 9:30 AM.
The /sbin/shutdown.sh file is a script that cleanly shuts down the virtual machines and it comes with the ESXi instance. The poweroff command is just "busybox poweroff".