The Addicks were leading through goals from Lawrie Wilson and Bradley Pritchard, either side of Craig Mackail-Smith's strike, but eight minutes after climbing off the bench, former Newcastle winger LuaLua marked his first appearance since October with the equaliser.
Just two minutes later the home fans were cheering again when Dale Stephens whipped in a cross which flew in at the far post with Wilson claiming the final touch.
It could have got worse for Brighton, but for Tomasz Kuszczak, who palmed Rob Hulse's header over and from the resulting corner, Michael Morrison headed too high.
But the visitors responded well and should have equalised when Mackail-Smith found Gordon Greer in front of goal, only for the defender to scoop his effort over from all of four yards out.
The leveller came in the 28th minute when Morrison made a mess of his clearing header and Mackail-Smith nipped in to tuck away his 10th goal of the season.
Brighton were still in the ascendancy after the break and Hamer parried a fierce drive from Will Buckley before Dobbie fired wide.
Dobbie was left kicking the post in frustration just before the hour mark after wasting another good chance.
Dean Hammond slipped in Buckley to cut the ball back for the former Swansea striker, who slid in to meet the ball but lifted it over the top.
Charlton had hardly troubled Kuszczak since their goal, but with their first genuine chance of the second half they went ahead again.
Johnnie Jackson's low cross ricocheted through the Brighton defence and Pritchard was on hand to sweep the ball into the net for his first league goal.
But three minutes later LuaLua grabbed a point for the Seagulls when his deflected shot wrong-footed Hamer and crashed into the net.