While your end goal is to drive a business outcome, you need to engage the team if you hope to have a successful business. And to fully engage the team you need to lead yourself well.
What drives full engagement? Leadership. People are watching you all the time. What are they watching for? How you lead yourself. People make a decision on a daily basis on how engaged they will be with you based on your level of influence with them individually. How you lead you determines what they see.