The visitors ended the game with 10 men after skipper Inigo Calderon received his marching orders for a dangerous high challenge on home midfielder Robbie Weir in the 88th minute, but the game had long slipped away from the League Two side.
The hosts had dumped out Wigan and QPR but goals from Rohan Ince, Kazenga Lua Lua and Craig Mackail-Smith justified Seagulls boss Sami Hyypia’s decision to make nine changes to the side held to a goalless draw by Championship strugglers Blackpool on Saturday.
Brighton needed a goalline clearance by Lewis Dunk to prevent Dominic Knowles from giving Burton a 15th minute lead, but Albion took the lead three minutes later.
Gary Gardner nodded Paddy McCourt’s free kick back across goal and Ince pounced with a powerful close-range header.
Lua Lua underlined Brighton’s supremacy with a classy solo goal in the 37th minute when he pounced on a loose ball on the halfway line before bursting clear and finding the bottom corner from 20 yards.
The Seagulls could have had a third five minutes after the restart but Jon McLaughlin produced a full-length save to keep out Chris O’Grady’s shot.
However, Burton’s fate was sealed in the 66th minute as Mackail-Smith hooked in a McCourt cross from six yards.