Defender Adam El-Abd gave the Seagulls the perfect start after only seven minutes, heading in a corner from Elliott Bennett.
Barnes doubled the advantage from the penalty spot on the half-hour after Troy Archibald-Henville bundled over Glenn Murray in the area.
Barnes put the seal on Brighton's fourth straight win by blasting his seventh of the season from a pass by Bennett with 13 minutes remaining.
Keeper Artur Krysiak produced fine saves from substitute Augustin Battipiedi, Barnes and Kazenga LuaLua in stoppage time to spare Exeter a heavier defeat.
Exeter, forced to make six changes after sickness swept through their camp, rarely threatened and James Norwood blazed their best opportunity wide.