Winger LuaLua, beginning a second stint on loan from Newcastle, broke the deadlock with a stunning free-kick four minutes after the break, his 25-yard shot carrying so much power that it went through the hands of goalkeeper David Martin.
The Seagulls made the League One points safe 15 minutes from time when LuaLua's magnificent cross was headed in at the far post by Murray.
MK Dons rarely threatened in front of goal and came closest when skipper Jermaine Easter was thwarted by goalkeeper Casper Ankergren midway through the second half at the Withdean on Saturday.
Murray should have done better early on when he headed wide at the near post following good work down the left by LuaLua.
LuaLua displayed explosive pace in setting up Murray in the 33rd minute, but the striker's effort from point-blank range struck the base of the post and went wide.