A solution that works:
Wrap the part of the document that needs this modified behavior with the code provided below. In my case the portion to wrap is a \part{} and some text following it.
\makeatletter\@openrightfalse
\part{Whatever}
Some text
\chapter{Foo}
\@openrighttrue\makeatother
The wrapped portion should also include the chapter at the beginning of which this behavior needs to stop. Otherwise LaTeX may generate an empty page before this chapter.
Source: folks at the #latex IRC channel on irc.freenode.net