Lewis Grabban went close for the Bees early on with a low drive from the edge of the area which Addicks goalkeeper Ross Worner did well to tip behind for a corner.
Therry Racon's stinging shot on the quarter hour produced a decent stop from Bees shot-stopper Richard Lee, while Scott Wagstaff should have done better after 20 minutes when he blazed over from inside the box.
Miguel Llera headed just over from a corner but a disappointing first half finished without a goal. Racon fired over from a good position early in the second half before Llera's 54th-minute header hit the crossbar.
The Charlton defender was denied again moments later with a header which produced an outstanding reaction save from Lee.
Legge claimed Llera had handled his header in the Charlton area but his penalty claims were ignored by the referee. But Legge had the last laugh when he headed home Myles Weston's corner to earn Brentford the bragging rights.