Calderon scored the opener eight minutes before the break with a clinical counter-attack before Elliott Bennett completed the victory late on.
Brighton's on-loan striker Kazenga LuaLua fired just wide inside three minutes after creating space down the left.
Calderon's goal followed a frenzy of action in the Brighton penalty area. Akpo Sodje and Therry Racon had their shots blocked on the line for Charlton after some good work by Johnnie Jackson.
The visitors immediately broke with great speed and Gary Dicker fed over-lapping Calderon down the right to fire beyond Rob Elliott.
Sodje responded with a late consolation in injury time but the home fans greeted the final whistle with boos.
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