I remember clearly the day my boss said to me, "I expect you to exert influence where you have no authority." I didn't like it; it seemed to me that if he wanted me to get the thing done, I should have the authority to do it.
But sometimes you won't have authority. Sometimes, on your team's behalf, you need to change behavior in another department. In those cases you need to lead without authority.
It won't be that hard if you already have influence, because influence is more effective than authority. You know that team member that everyone listens to, sometimes more than they listen to you? That guy, or gal, has influence. Influence comes from credibility, from a reputation that makes people trust you. If you have it, all you have to do is talk.
If you don't have influence, then you have to build your case. Start with the idealistic: How what you want is good for the world, will secure the future of the company, may even shrink the hole in the ozone layer. Then move on to what's in it for the other department; it has to somehow be good for them or they won't listen.
It sounds cynical, but the bottom line is other departments aren't likely to change just to help your team, and without authority you can't make them. You have to persuade. And it takes a better leader to do that than to command.