The play-off semi-final remains firmly in the balance after a dramatic night at the City Ground which began with a red card for Swansea defender Neil Taylor.
Forest pressed hard to make the most of their man advantage but could never relax at the back as the visitors continued to show plenty of attacking endeavour of their own.
It was the away fans who were happier when referee Mike Dean blew thr final whistle but although Swansea will now start as favourites to make it to the Wembley final the tie remains hard to call ahead of Monday night's second leg.
"It was a brilliant performance. To lose a man so quickly is obviously difficult," visiting boss Brendan Rodgers said afterwards.
"Nottingham Forest are an outstanding side but I thought my players deserve all the credit, they were absolutely brilliant and deserve all the plaudits they get."
Opposite number Billy Davies commented: "I said before the game, win lose or draw, it is only half-time, and that is still the case.
"There is still lots to play for and I am full of optimism for the second game. It is still a very open game that can go either way."