Zoltan Gera gave West Brom a 30th-minute lead before Republic of Ireland striker Shane Long capitalised on Simon Mignolet’s mistake to double the visitors’ advantage just before half-time.
However, Sunderland fought back, with Craig Gardner scoring a free-kick in the 73rd minute to offer the Black Cats hope before Romelu Lukaku scored from the spot to restore the Baggies’ two-goal cushion.
There was still time for more drama as Stephane Sessegnon reduced the deficit with three minutes remaining, but West Brom substitute Marc-Antoine Fortune sealed a 4-2 win which pushed Clarke’s men into third spot.
“All I know is up until now, we have done very well,” Clarke told Sky Sports.
“We have had a lot of plaudits and the players deserve it because so far, we have been a really good team.
“But you don’t get carried away in the Premier League. We are still this side of Christmas, there are a lot of games to be played, a lot of points to be fought for.
“Our focus is on Wednesday night against Swansea, that’s as far ahead as we look.
“I’m a realist. I knew the squad of players I was taking over was a good squad, I knew it was a squad comfortable in the Premier League.
“They had finished mid-table and mid-table with 47 points both seasons. We knew we had added some good players to the squad. So far, we have done okay.”