Leeds started slowly and Brighton broke a three-game goal drought by taking the lead through a Pascal Gross penalty in the 14th minute.
Ezgjan Alioski was penalised for bringing down Danny Welbeck in the area and Gross found the bottom left corner with the resulting spot-kick.
Brighton remained 1-0 ahead at the break but should have doubled their lead in the 40th minute.
Seagulls forward Leandro Trossard blazed high and wide with the goal gaping after Leeds cheaply conceded possession deep inside their own half.
Brighton finally doubled their advantage to 2-0 with 11 minutes to play courtesy of a sublime goal from Welbeck.
After Pascal Struijk cleared into the air inside the Leeds area, Welbeck executed a perfect 'Cruyff/Gross turn' as the ball dropped before firing into the bottom right corner.
Scroll down and click through to see who shone and who struggled for Brighton