I use WGet. Here are the instructions for forming the team city URL. You can do a WGet in powershell, but if you only wanted powershell for this functionality, you can just use a plain wget utility for windows.
EDIT: Here is an example from our QA deployment (names changed to protect the guilty):
"C:\Program Files (x86)\NcFTP\wget.exe" "http://teamcityserver.domain.com:8111/guestAuth/repository/download/bt6/.lastFinished/Artificat.ear"
The location of the wget isn't relevant, that is just where it happens to be. The guestAuth part of the parameter specifies the authentication type (in our case we enabled guest authorization to not have to bother with passwords - it is an internal server only anyway and protected by firewalls). The options are in the documentation I linked to.
The other interesting feature of the parameters is the bt6. That is the unique key of the build, and is different for every project. You can discover what it is by navigating the team city website to the configuration of that build - it will be there. There are also instructions for referencing the configuration by name, but we found that was too verbose to bother with.