The victory took the Baggies to 10th in the Premier League - just four points off third-placed Manchester City, although it took an Esteban Cambiasso own goal to settle the tie.
"It means a lot. It is a difficult place to come to and we are the first team to win here [this season]," boss Alan Irvine told BBC Sport after the game.
"It was a complete team performance. We needed a threat up front and we did that. At the back we were solid against some really difficult forwards to play against.
"Three points. Clean sheet. It's a great feeling for us and it gives us a platform to go into the next game - Newcastle at home - which will be really difficult for us.
"I said all along it was going to take a bit of time, but it was important to find the best way of playing for our group of players and we are getting closer to that."
There was no Irvine on Twitter but Berahino and Gardner both had their say, while goalkeeping coach Dean Kiely also tweeted after the win: