Watched by their biggest gate of the season, Orient were second best for long spells to a resilient Forest team, but it was a slip by home keeper Stuart Nelson that presented Forest with their goal.
Agogo latched on to a loose ball on the edge of the O's penalty area and saw his tame shot slip through Nelson's hands into the net.
Earlier, in a first half high on work-rate, there were few clear cut chances at either end.
Orient started well and their best chance of the first 45 minutes arrived in the opening stages when skipper Stephen Purches crossed from the right and the ball fell invitingly for Jason Demetriou, but he fired straight at Forest keeper Paul Smith.
As the half progressed Forest took a grip on the game but, apart from a few half chances, they were rarely able to test home keeper Nelson as Orient defended well.
The best Forest chance fell to striker Grant Holt on 28 minutes, but his shot was blocked by the impressive Purches.
After the interval, Forest continued to dominate and Nelson made a great save from a Kris Commons free-kick on 54 minutes, before Agogo popped up with the all-important winner.
The nearest Orient came to an equaliser was on 69 minutes when Forest defender Wes Morgan, who was otherwise so solid at the back, sent a clearance against the foot of his own post.
In a desperate bid to salvage a point Orient boss Martin Ling threw three substitutes into the fray, but Forest defended doggedly and always looked likely to stretch their advantage on the break.