In what was a clash of cultures in Wales, the Swans - managed by former Walsall coach Russell Martin - played a possession-based game throughout.
Valerian's Ismael's tenacious Albion meanwhile looked to counter-press with intensity and aggression.
Karlan Grant's fifth goal in as many games put the Baggies in front after just 52 seconds.
After the interval, though, Swansea were the better of the two teams.
Joel Piroe levelled for the hosts when he beat the offside trap.
Then with less than 10 minutes to go, fellow ex-Saddler Jamie Paterson won it with an excellent individual goal - which came from a sloppy mistake from Darnell Furlong.
And Ismael felt that mistake cost his side a point.
"We are disappointed to lose the game - especially with another mistake," the boss said.
"It was the same case against Stoke, and they punished us. We started well, like we wanted, with a good pressing situation, we controlled it and forced a lot of long balls.
"Swansea didn’t create a big chance, and our problem throughout the game was our transition. We didn’t keep the ball in the pocket. We lost the ball too quickly.
"My expectation is that we come quickly into the final third and that we push the line high and have an aggressive defence so that the opponent cannot push out of pressure. We didn’t make it well, and it’s the reason Swansea came back in the game and they started better in the second half.
"You need to find a way to stay compact and organised.
"The conceded goal gave them a second breath to come back into the game.
"At that point we had a big chance with Matt Phillips, to take the lead again, big save from the keeper. It’s a game on the edge at that point, and it’s important to stay in the game.
"At the end we made the big mistake, and it’s the reason we lost.
"But we don’t need to overreact because we play the next game on Saturday and we need a reaction.
"I said to the guys, keep the mind-set and make sure we have the right reaction - it’s another way to play, another game, a battle and we need the right mentality."
Albion have now lost two of their last three Championship games.
But Ismael says every Championship team will endure a wobble at some point.
"This is the Championship - everything comes quickly," the boss added.
"Take the game one by one. Everyone struggles, the quality is so high.
"The winter time will come and things will change. We don't overreact.
"It’s just to make sure we stay on the right path and it’s all about the reaction on Saturday."