The visitors wasted no time in taking the lead when after only three minutes Chris Cohen's corner was flicked on to the back post by Grant Holt, where Paul Edwards managed to stab the ball into the roof of his own net.
A comical error by Paul Smith almost cost Forest their lead when his throw hit the back of the referee to give Danny Whitaker the chance to shoot, but his effort fell wide of the mark.
Martin Foyle was forced re-shuffle his backline when Keith Lowe was unable to continue in the 26th minute allowing Mark McGregor to come in at right-back.
After a long spell with limited opportunities for both sides, Paul Harsley was given the chance to equalise in the 42nd minute but his shot from 12 yards skimmed past Smith's right post.
Despite picking up a booking seconds earlier, Ashley Westwood forced a superb save from Smith just before the break when his header almost found the net.
The Valiants continued their hot streak after half-time when David McGoldrick set up Whitaker for a shot on the edge of the box, but Smith proved himself once again with a great stop despite the effort taking a deflection.
Forest should have doubled their lead in the 49th minute when another Cohen corner found its target in the shape of Holt, but the forward sent his header clear over the crossbar.
Holt remained lively throughout the second half, but was restricted to a long-range effort in the 76th minute, when he let fly with a 20-yard strike that rocketed into the stand behind the goal.
Calderwood's men made sure of the win in 87th minute when substitute Kris Commons supplied Luke Chambers who sent the ball confidently past a helpless Joe Anyon from ten yards.