A sensational start to the game saw Taylor dismissed after only 52 seconds. The Swans defender caught Lewis McGugan on the thigh with his studs as both players went into the challenge with raised feet just inside the Swansea half on the left touchline.
McGugan got to the ball first and, with the home crowd baying for blood, referee Mike Dean pulled out his red card.
Swansea manager Brendan Rodgers was forced into an unexpectedly early reshuffle. Scottish striker Stephen Dobbie was the player sacrificed as Garry Monk was introduced from the bench in the fourth minute. However, while Forest struggled to break down ten men, the Welsh side were unfazed by their numerical disadvantage and created the better chances in the first half.
Fabio Borini was the main threat. The on-loan Chelsea forward forced Forest goalkeeper Lee Camp into saves on three occasions.
In the 20th minute he beat Luke Chambers for pace down the left side, cut into the penalty area and Camp had to rush from his six-yard box to smother the danger. Soon afterwards, he went even closer with a superb 25-yard free-kick. His run was almost Cristiano Ronaldo-esque and his shot was not too unlike that of the world's most expensive player either as he struck the ball over the wall and forced Camp to help it over the bar.
Borini worked Camp again on the half-hour, shooting through Brendan Moloney's legs after It took Forest 36 minutes to muster an effort of their own. Kris Boyd got free down the right-hand side. His low cross was met by the penalty spot by Robert Earnshaw, who controlled his half-volley with the side of his foot but Dorus De Vries dived to his right and palmed the ball away.
Forest continued after the break where they had left off in the first half. A dipping 25-yard shot from McGugan was palmed back into the danger area by De Vries before the ball. McGugan then produced a defence-splitting pass to pick out Chris Cohen, but his pull-back to the edge of the box was blasted over by Earnshaw in the 55th minute.
Forest thought they had made the breakthrough after 68 minutes when Earnshaw headed home McGugan's corner, but the Wales international was flagged offside.
Swansea immediately went on the counter-attack. Dyer darted down the right side and struck an early shot from the edge of the area that brought a superb one-handed save from Camp as he got down to his left.Forest continued to search for a crucial goal to take to South Wales but it was not forthcoming, with Chambers heading harmlessly over from another Cohen cross in injury time.
Nottingham Forest: Camp, Moloney, Morgan, Chambers, Gunter, Anderson, McKenna (McCleary 72), McGugan, Cohen, Earnshaw (Tyson 71), Boyd (Tudgay 77). Subs Not Used: Smith, McGoldrick, Majewski, Lynch..
Swansea: De Vries, Rangel, Williams, Tate, Taylor, Britton, Dobbie (Monk 4), Allen (Gower 72), Dyer, Borini (Moore 56), Sinclair. Subs Not Used: Makalambay, Pratley, Orlandi, Serran.