I have a closed-source application that calls an unmodified GPL binary from the command line. I need to distribute the GPL binary with my application. Can I include it in the installer while keep my application closed source and comply with the GPL license terms? Or do I need a different method of distribution for the binary?
Yes you can distribute a GPL'ed binary.
You should probably note somewhere in your license or help-about that the binary is GPLed and where to get the source. If you haven't modified it - you don't have to provide the source.
There is a link to a compliance guide, although this takes a very 'pro GPL' line suggesting that you have to do an awful lot of work if you aren't GPL.
edit: Perhaps a good test is the original 'freedom' aim of the GPL.
Does your usage allow the user to swap out the GPL'ed part for a newer or their own version?
Do you just use the standard command line call of the GPL binary or do you rely on a particular binary build (by some weird in memory patching or DLL loading technique), or deliberately lock it to 'your' binary with eg. checksums ?
If your software can't work without the GPL software, this is considered as a combination. And therefore, you must make your own software GPL.
GPL is more strict than LGPL that allows referencing the binaries without having to release your software as GPL or LGPL.
Linking ABC statically or dynamically with other modules is making a combined work based on ABC. Thus, the terms and conditions of the GNU General Public License cover the whole combination
http://www.gnu.org/licenses/gpl-faq.html#LinkingOverControlledInterface
If I was you, I would contact the authors of the GPL software and ask them a written permission to do what you have to do. I see no valid reason why they would say no.