He made a series of top-class saves to keep the Swans at bay, but if they continue in this form they must have a fine chance of being in the promotion frame at the end of the season.
City almost took the lead in the fifth minute after a fine run through the middle by new Dutch signing Ferrie Bodde.
He passed wide to Jason Scotland whose cross looked as though it was going into the net until Smith managed to scoop the ball around the post.
Smith was once again in the action saving two shots from Andy Robinson as the Swans piled forward looking for the early goal.
Midway through the half Julian Bennett brought down Leon Britton just outside the area, but once again the over-worked Smith came to his side's rescue, beating out Angel Zaragoza Rangel's goal-bound shot.
Forest gradually stemmed the tide and after Scotland missed a gilt-edged chance by shooting tamely wide, Sammy Clingan had Dorus de Vries diving low to his left to push behind a 20-yard drive.
The visitors came out for the second half looking more determined, yet it was Smith once again who was first in the action going down to save from Robinson.
Twice in the closing minutes the post came to the visitors' rescue when a shot from Scotland struck the outside with Smith beaten and then a header from Bodde was deflected by a defender onto the post and behind for an unproductive corner.
Then it was Rangel's turn to fire in a blistering shot that Smith somehow managed to palm into the air and gather at the second attempt to earn an undeserved point for his side.