Arsenal came out a different side in the second period and pulled one back with a banana-shot from Stephen Bradley.
Forest were on the ropes and an Arsenal equaliser looked more and more likely. The breakthrough came when Adam Birchall's shot rebounded off Barry Roche's crossbar and Stathis Tavlaridis tapped in unmarked.
The Gunners sealed the three points after Juan struck a low left-footed shot into the corner shortly before the end.