The hosts themselves had gone five league games without defeat but fell behind early on courtesy of a moment of Liam Trotter brilliance.
After cutting in from the left and evading two Forest challenges, Trotter directed a 20-yard curler past Lee Camp in the home net.
Experienced midfielder Andy Reid tested Forde with a succession of set pieces as Forest grew into the match following their goal.
Millwall were still able to create chances of their own though, and nearly went ahead when Darius Henderson's close-range header flew narrowly over the crossbar.
Henderson did find the target on the hour mark as Millwall took the lead for a second time courtesy of his header from James Henry's precise cross.
In-form Chris Wood made the result secure when he applied the finish to a swift Lions counter-attack with a deflected low shot past Camp.