How do I stop a coworker who is monologuing during a meeting?

A reader writes:

I would love some feedback/advice on how to deal with a difficult coworker in a different department. We work with this department to handle legal matters for our group, so we have to liaise with them sometimes.

He is a terrible communicator. Every time we meet, he goes off on long, irrelevant tangents that are the same or similar every time. We usually have a lot to cover in these meetings, and I don’t like to waste time when things need to get done.

At our most recent meeting, he had rescheduled several times and then at the last minute decided to call in instead of attending in person (so I was already annoyed). After being asked simple, direct questions, he started talking about something that was not relevant. In the middle of his monologue, I interrupted him and said, “Thank you, but I’d like to keep going, we have a lot to cover.”

We moved on, but we could tell he was disappointed, and two of my coworkers in the room later told me I shouldn’t have done that. He is senior to me and his role is really important, and I don’t want to be rude. But I also don’t want to sit in countless meetings where things don’t get done because this person can’t do their job effectively. help!

I Inc. today. I’m answering this question here, where I’m revisiting letters that are buried in the archives here from years ago (and sometimes updating/expanding their answers). You You can read it here.