Brighton's Adam Chicksen (right) challenges for possession[GETTY]
Victory was marred only by Inigo Calderon’s sending-off in added time for a high tackle on Robbie Weir.
Rohan Ince put the Seagulls ahead with an 18th-minute header after Gary Gardner nodded back Paddy McCourt’s free kick.
Talking Points - Gameweek 6
Kazenga LuaLua capped a fine individual display with a powerful 37th-minute run and shot to give Brighton the breathing space they needed.
Craig Mackail-Smith finally put the skids under League Two Burton’s cup run – which included victories against Wigan and QPR – by hooking home McCourt’s cross from close range in the 66th minute.
Burton were left to rue a golden early chance, Lewis Dunk clearing off the line to foil Dominic Knowles.
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