Bersant Celina came off the bench to earn Swansea a 2-1 triumph over Sheffield Wednesday at the Liberty Stadium.
It looked as if the Owls were going to claim their first away win for more than two months when Marco Matias punished Joe Rodon for a defensive error after 63 minutes.
But Celina played a key role as two goals in a minute from the substitute and Wayne Routledge turned the match in Swansea's favour to pile more pressure on Wednesday manager Jos Luhukay.
Both sides had to wrestle with conditions early on as the match got under way amidst swirling wind and driving rain in South Wales.
Routledge, who marked his first start of the season with a goal inside 40 seconds last week, looked keen to build on his clinical comeback by troubling the Owls defence.
He had already made some incisive runs down his right wing before he latched on to a flick-on from Oli McBurnie and dragged a shot just wide of the post.
For all their possession, Swansea almost went behind when they switched off at the back and let Lucas Joao get the wrong side of Leroy Fer in the Swans' penalty area.
The Portuguese striker had a clear sight at Erwin Mulder's goal, but let the Swans off the hook with a shot that flew wide.
After weathering the Swansea storm in the first half, Wednesday gave themselves an opportunity to claim a rare away win after 63 minutes.
Rodon had got away with a defensive error when Joao curled a shot wide of the upright, but he was punished when he gave the ball away cheaply for a second time on the edge of his own box.
The 21-year-old was robbed of possession by Matias, who kept his cool to drill a shot post Mulder into the back of the net.
However, the inspired introduction of Celina after 66 minutes turned the game in Swansea's favour.
The former Manchester City academy graduate produced a composed finish to level the scores after 71 minutes after Barrie McKay slipped Roberts in behind the defence to make the final pass.
Then less than a minute later Celina picked up the ball in the middle of the pitch and lifted an inch-perfect pass over the defence for Routledge to chase.
The 33-year-old took the ball in his stride and fired a low shot through the legs of Cameron Dawson and into the back of the net to complete the comeback.
The managers
Graham Potter: "It's fantastic for the players and the supporters. It was a pretty awful afternoon in terms of weather. The support was great for us. They stuck with us and helped us. I think we started off well in difficult conditions but, as in anything, the opposition came back into it a little bit.
"Overall, in that type of afternoon there's going to be a couple of mistakes. Maybe there was a little bit of that in the first goal and it got nervy for a few minutes but I thought overall we deserved the victory."
Jos Luhukay: "It's very hard to take, it is totally frustrating to give away a 1-0 lead in a couple of minutes. Swansea had no chance to score but we didn't have any discipline or concentration to hold the lead. In a couple of minutes we gave everything away. We didn't defend down our left side twice and that is not acceptable, you have to run with your opponent, I have tried to coach this three or four times but it is not going in their heads.
"I am so angry because the players are showing no proof of what we are doing. It is not the first time we give a 1-0 lead away for the opponents to score two goals. How many times has this happened? When the players don't learn from this situation then you won't win games. Maybe the players can give the answers."