Long story short: No.
The third-party app approach exploits privilege-escalation vulnerabilities in the Android OS. The app is required to package/run that exploit. You can't go that route without the app. This approach is also a hack (literally), so you may run into unexpected issues along the way. It's generally not really recommended unless there is no other way (bootloader can't be unlocked, etc.).
Rooting the right way always involves flashing a custom recovery, which can then be used to flash software that wasn't signed by the manufacturer (like superuser.zip).
With few exceptions those are the ways to root a device.
What device do you have, and/or why don't you want to use either of those rooting methods?
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