Solution:
Yes, what you need is WordPress Multisite (previously known as WordPress MU, or WPMU).
Plus the Domain Mapping plugin, which will take care of making the sub-site work as a Top Level Domain.
Multisite is installed to work with sub-domains or with folders: http://subsite.example.com or http://example.com/subsite. What the plugin does is to map something like http://client.net or http://microsite.client.net to a selected sub-site. It’s practically transparent, the visitor doesn’t know he’s looking at a sub-site.
Check the wiki with Multisite resources at WordPress Answers.
Hints: 1) It’s extremely important to watch exactly what plugins and themes you’re installing. Reputable sources, stable code. 2) If backup and security measures are important in any site, in Multisite multiply that by the number of sites running and a bit more.