Andrew Mumford's extra-time winner dumped holders Swansea City out of the Premier Cup at the quarter-final stage.
The ex-Swans midfielder struck from 20 yards four minutes from time to seal a famous win for the Welsh Premier side.
Kyle Graves put Swansea ahead early in the second-half after a one-two with Lee Trundle, but Richard French replied with short-range header on 75 minutes.
Dane Williams hit the Swansea crossbar in extra-time before substitute Mumford struck a low drive past Willy Gueret.
Port Talbot join fellow Welsh Premier side The New Saints in the next round, with the two other quarter-finals between Carmarthen and Cardiff, and Newport County and Wrexham still to be played.
Port Talbot Town manager Wayne Davies:
"I'm immensely proud of the players. They did a fantastic job.
"They've not only beaten a strong Swansea side but matched them in all areas of the pitch. I don't think anyone could deny that.
"The boys at the back were outstanding again. I thought we were the better side in the first 45 minutes and that gave us the belief that we could beat them."
Swansea City manager Kenny Jackett:
"The game could've gone either way but it was disappointing performance from start to finish from us.
"We never got going. In extra-time I was picking my penalty takers before they scored. Lee Trundle had a good chance at the end but it didn't quite go for us.
"We should've gone on to win after taking the lead, but fair play to Port Talbot they played well."
Port Talbot Town: Kristian Rogers, Dylan Blain, Dyfan Pierce, Craig Hanford, Mathew Rees (capt), Lee Surman, Lee John, Dane Williams (Andrew Mumford 111), Chad Bond (Martin Rose 60), Dean Johnston, Scott Barrow (Richard French 67).
Subs: Nicky Jones, Tom Hopper.
Goal: French 74, Mumford 116.
Swansea City: Willy Gueret, Izzy Iriekpen, Steve Watt (Adebayo Akinfenwa 75), Marcos Painter, Kyle Graves, Alan Tate (cap), Ian Craney, Joe Allen (Rory Fallon 46), Tom Williams, Lee Trundle, Chris Jones (Thomas Butler 65).
Subs: James Burgin, Adebayo Akinfenwa, Richard Duffy.
Goal: Graves 58.