The Isaiah4110 answer is not the best way if you don´t need a UI.
The simplest way to execute the exe file target you are installing through the MSI file produced by Wix is with a custom action type 18 (identifying the action by FileKey), here you are a complete example:
<Fragment>
<ComponentGroup Id="ProductComponents" Directory="INSTALLFOLDER">
<Component Id="TargetProgram" Guid="f757ff43-0266-483a-8749-ec796cba4b25" >
<File Id="EXE" Source="C:\SetupProject\Includes\TargetProgram.exe" />
</Component>
</ComponentGroup>
<CustomAction Id="EXECUTE_AFTER_FINALIZE"
Execute="immediate"
Impersonate="no"
Return="asyncNoWait"
FileKey="EXE"
ExeCommand="" />
<InstallExecuteSequence>
<Custom Action="EXECUTE_AFTER_FINALIZE" After="InstallFinalize">NOT Installed</Custom>
</InstallExecuteSequence>
</Fragment>