Stephane Sessegnon and Morgan Amalfitano scored either side of Liam Ridgewell's effort, and Clarke was happy that his side finally got off the mark with their first Premier League win this season.
"We played well in the game," Clarke told Sky Sports. "I thought we started slowly. Sunderland started quite bright and passed the ball around quite well.
"We started anxiously but the goal settled us down. We got the breaks at the right time as well. I thought today we played some good football."
While Sunderland started perhaps the brighter, Sessegnon struck in the 20th minute - only the Baggies' second goal this season - and Clarke felt that was the game's turning point.
"It was important that we found our rhythm in the game, it took us a little bit longer to find that than maybe it should have done.
"Credit to Sunderland as they started well, but we kept our patience."
On debut boys Sessegnon and Amalfitano, Clarke was happy that his summer captures have started to repay his faith already.
"For Stephane it's great that he gets off the mark on his debut. He showed good respect to the Sunderland fans too.
"Morgan was good as well. I said when we signed him he might surprise a few people. He's a proper wide midfielder and creates so many chances."
West Brom's slow start this season shocked a few after an impressive eighth-placed finish last time out, but Clarke was quick to dismiss early-season fears.
"Last season is history. For us the most pleasing fact is that after a difficult start good signs for the future are evident."