Running SCCM 2012 R2 environment.

Users currently running Office 2010. I need to ONLY upgrade Outlook from 2010 to 2013. What is the best way in doing this? 

Anyone experienced this before? 

Create an application for Outlook 2010 and Outlook 2013, you could use Outlook.exe's version info as an detection method. Configure Outlook 2013 to supersede the Outlook 2010 and you're good to go on with the deployment.

Are you talking about Application Supersedence? I have not attempted this feature yet. Any good places to start?

I have 200 machines I need to update and I obviously want the fastest method possible...

To install only Outlook 2013 You should use Office 2013 Customization Tool (https://technet.microsoft.com/en-us/library/cc179097.aspx?f=255&MSPPError=-2147217396). There You will be able to configure that only Outlook is ugpraded and other Office components are not upgraded.

Also be sure to test upgrade process thoroughly, before rolling out the ugprade to all machines.

Use office customisation tool to disable other office components (like excel,work,powerpoint etc) except outlook and use outlookmui.msi file as msi detection from outlook.en-us folder or you can also entire office suite msi ( standardww.msi) from standard.ww folder.

Also create vbscript or powershell to notify prompt to close the outlook if they are running so it avoids the disruption before migrating outlook. Use the powershell app deployment toolkit to customize the prompt messages more via https://psappdeploytoolkit.codeplex.com/