Since I haven't found a way to solely rely on MS-installed command line tools, I'll list third party solutions.
WinApiExec
WinApiExec enables the user to call the Windows API from the command line. The 32bit executable is only 3.5KB in size (x64: 5.5KB) and therefore ridiculously small, introducing as little overhead as probably possible.
winapiexec.exe virtdisk.dll@OpenVirtualDisk $a:2,0 "C:\Example Path\Test.vhd" 262144 0 0 $b:4, virtdisk.dll@DetachVirtualDisk $$:7@0 0 0
vMount
vMount supports quite a few VHD-related functions. Its size (x86: 432KB; x64: 2.53MB) is rather huge for merely calling WinApi, so it's not a solution for my scenario, but might be useful to other people.
vmount detach \\.\PhysicalDriveX
DiskPart
For the sake of completeness DiskPart shall be mentioned, too. It supports a great deal of disk-related features, but has a rather sluggish way of going about it to automate the otherwise necessary user input for scripting purposes. It's also the only tool on the list that will be trapped in a loop if you accidentally run the script without elevated rights.
Save the following two lines into a text file:
vdisk file="C:\Example Path\Test.vhd" detach vdisk
Now, Dism can parse the text file as a form of unattended answer file:
DISKPART /s C:\Path_to\Name_Of_Textfile.txt