Conor Gallagher scored the game's only goal when he drove through a crowded box early in the first half.
Baggies boss Slaven Bilic said afterwards, "It's a massively important win. This was THE game. There are enough games after this one, but it was very important - crucial - for both teams to win the game. That's why we saw quite an open game with nearly 40 shots and many chances. We're delighted that we won the game. We showed the quality and showed character. We had chances to go two up and make it a little easier for us. I told the guys that now we have to rest, build on this and continue to improve.
"The guys are reading the papers. Everybody's asking when are you going to get your first win. That's why it was incredibly important for us to go over that block. I see this as more than three points, because it's our first win. Second, we've done it against a team who is down there with us. It's a great boost for our confidence and for the games that are coming."