Millwall looked the sharper of the two sides for much of the first half, with Aiden O'Brien coming close to an early goal when he fired wide after Brighton had twice missed the chance to clear a cross.
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Lee Gregory caused most of the problems for the Brighton defence, and he almost created the opener by latching on to a long ball before picking out Martyn Woolford, who could only find the side-netting.
A long spell on top either side of the break handed the control to Brighton, but Millwall did a fine job of keeping the chances to a minimum.
Forde couldn't get close to a free kick from Joe Bennett as Millwall were rescued by the woodwork as the ball rattled the crossbar.
Best was kept on the fringes of the match for long spells, but he continued to look a threat as he found the space to head wide of the target from an inviting Bruno cross.
Substitute Kazenga LuaLua almost snatched a winner for Brighton late on as his effort from the edge of the box drifted just past the target.