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The first chance of the game fell to Henri Lansbury on five minutes, but his shot was saved well by Adam Bogdan. The Hungarian then showed quick reactions to keep out Radoslaw Majewski's effort from the rebound.
Lansbury had his second chance of the game on 14 minutes, but he dragged his shot wide of the post.
The home side dominated proceedings and had another two chances through Majewski and Simon Cox, but they were denied by an in-form Bogdan.
Bogdan pulled off another fine save on 49 minutes, keeping Reid's 30-yard free kick out.
Forest finally beat Bogdan on 59 minutes when Reid struck a volley into the far corner from inside the area to make it 1-0.
The away side went down to 10 men on 80 minutes when Marcos Alonso received his second yellow for a mistimed challenge.