The Baggies' opening goal was scored by Stephane Sessegnon, the player the Black Cats sold to the midlands club earlier this month amid some acrimony.
The Scot said: "It was not quite perfect but obviously a good afternoon for us. It was a game we felt we should win.
"Once we got our noses in front we had a good control of the game and circumstances went for us as well - at 1-0, before the nervous last 15 minutes, they lost Steven Fletcher. That helps.
"Immediately we made it 2-0. All in all, a good afternoon."
Clarke was also pleased with the immediate impact made by Sessegnon, who refused to celebrate his goal.
He said: "He did what we brought him here to do. He is clever on the ball, he is bright, he is an entertainer.
"He has got some goals in him as well, so a pleasing debut for him.
"I think he showed respect to Sunderland. The fans liked him and loved him as a player.
"He is quite an engaging character and he chose not to celebrate. That's fine. If he wants us to celebrate more than him I'm happy with that."
- Sports & Recreation
- Stephane Sessegnon
- Liam Ridgewell
- Morgan Amalfitano