The first half saw Swansea control the game despite having Neil Taylor sent off inside 2 mins, but in the second half they were happy to soak up pressure and looked to attack on the break.
Forest should have been awarded a penalty but a handball was missed and while they enjoyed the majority of the second half they could not find a way past Dorus de Vries.
Nathan Dyer, awarded Sky's man of the match award, nearly scored with a breakaway goal but Swansea will go home very happy with their evenings work.
Next up Reading v Cardiff. Friday, 7:45pm.