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Kieffer Moore had a rare attack for the away side following sloppy play by Forest, but he could only drag his effort wide.
The home side got the goal that their start deserved with 16 minutes played. Paterson collected the ball behind the Yeovil defence and saw his shot hit Byron Webster on its way in.
Stech produced a good save down low to his right to turn Henri Lansbury's shot round the post in the opening stages of the second half.
Paterson then hit the post with an effort from inside the penalty area as the hosts began to turn the screw.
The Glovers tried hard to find an equaliser as Joe Edwards's curling effort was well saved by Darlow. However, Forest wrapped up the win when Rafik Djebbour scored a debut goal deep into stoppage time.