The game began in a rather scrappy manner and Jake Forster-Caskey was booked in the 10th minute for a late challenge.
Shamir Fenelon then fired a shot towards goal, but Westwood was also equal to his effort.
Sheffield Wednesday rarely threatened in an attacking sense, but a moment of quality from Giles Coke gave the visitors the lead shortly before the break. The midfielder struck a long-range effort with his left foot which curled beyond the reach of David Stockdale.
Just five minutes after the break, things went from bad to worse for the home side as Andrew Crofts was shown a straight red card for a rash challenge.
Brighton's frustration was evident as LuaLua was cautioned late on for dissent and Wednesday held on to secure an important opening-day victory.