Under-pressure manager Pepe Mel felt "blessed" to finally get a win under his belt as West Brom manager.
The Baggies upset the odds at the Liberty Stadium to come from behind and earn a 2-1 win which saw them move three points clear of the Barclays Premier League relegation zone.
It was their first away win since September 28, when they upset Manchester United at Old Trafford, and their first victory of any kind since beating Newcastle on New Year's Day.
Spaniard Mel, who took charge on January 9, said: "I am blessed. For the fans, for the players, we need to win and in football, confidence is all.
"The players need to win and now it's different, I hope."
Mel felt his midfield was over-run by Swansea in the first half, but thought the tactical changes he made shifted the momentum.
Revealing what he spoke about at half-time, he added: "We talked about the problems, talked about the football, talked about the future face to face, and it's only 45 minutes and we need to change. The football players at West Brom are intelligent.
"The pressure is the same for all the countries - in Spain, in England, Germany it's the same.
"My work is dangerous. Head coach is a difficult job, but the most important in football is the player."
Swansea started with a bang as Belgian winger Roland Lamah put them in front after less than two minutes, beating Steven Reid on the by-line before curling the ball past England international Ben Foster.
The Baggies took hold of the game in the second half and Congolese midfielder Youssouf Mulumbu's side-footed effort from 20 yards nabbed the much-needed three points after Stephane Sessegnon levelled from outside the box on 53 minutes.
Garry Monk was perplexed by Swansea's capitulation in the second half.
"You never have it won by half-time, whatever game you play in," he said. "The way we played first half was pretty much exactly how we wanted them to play.
"They carried it out, we were getting crosses, we were causing problems, we were getting chances and probably could have taken a few more, so probably should have taken more from the first half.
"You've got them on the ropes and if you don't knock them out, you're always open to them coming back into the match and that's exactly what happened. (It was a) very good first half and very poor second half.
"The way we come out second half was very sloppy, very poor. Our passing was poor, our touches invited West Brom onto us and then unfortunately the second goal in these sorts of games is always crucial.
"They got the second one, which gave them the impetus going forward and unfortunately we conceded a second. I don't think we deserved to lose the game, but we definitely didn't deserve to win it after that second-half performance."
West Brom are now 16th, with the Swans one point and two places better off in 14th.