It is possible to install drivers using command-line tools available in Windows Server core. This article describes how to install network driver.
Mount Parallels Tools ISO to the affected virtual machine:
~# prlctl set VM_NAME --device-set cdrom0 --connect --enable --image /usr/share/parallels-server/tools/prl-tools-win.iso
Inside virtual machine change directory to the optical drive, e.g.:
This will install all nescesary Parallels Tools components.
If only network driver is required, it can be installed from the disk:
Pnputil.exe -i -a D:\Drivers\prl_eth5\prl_eth5.inf`