There was a delay early in the match as referee Andre Marriner was forced off with an injury after just seven minutes, resulting in the fourth official taking his place.
After a quiet opening 20 minutes, the hosts started to see more of the ball, and managed to break the deadlock when Chris Burke squared the ball to Fryatt, who coolly slotted home.
Sebastien Pocognoli tried to set up a quick equaliser down the other end for the Baggies, but there was no-one in the box to meet his cross.
Fryatt, confident from his earlier effort, tried his luck from distance shortly before the break, but the 30-yard strike failed the trouble the West Brom goal.
Graham Dorrans had a chance at the start of the second half for the visitors, but his 20-yard drive was tipped away by Karl Darlow.
However, Forest started to dominate again, almost resulting in a second for Fryatt when he tried to tap in from an Andy Reid cross, missing by inches.
Victor Anichebe came close to getting West Brom back on level terms with 15 minutes to go, but his header was cleared off the line.
Dawson also had a chance in the closing stages, but his header from a Dorrans corner went wide of the near post, allowing the home side to hold on for the win over their Premier League opponents.