It was only Albion's second league loss of the season, but the home side were full value for their victory.
Pools took the lead on 23 minutes, Neil Austin starting and finishing the move. His firm tackle on the halfway line won possession and he kept charging forward after feeding James Brown. When Brown's deep cross was nodded across goal by Antony Sweeney, the right-back had an empty net to nod into.
Brighton started the second half well and levelled when lively substitute Kazenga LuaLua crossed for Gary Dicker to fire home.
But Gary Liddle restored the lead in the 71st minute with a low shot after Sam Collins' long throw was not cleared.
Five minutes later, Liddle was on the receiving end of a strong challenge from Liam Bridcutt and the visiting midfielder was sent off by referee Russell Booth. The points were sealed after 84 minutes when Leon McSweeney's cross was headed in by James Poole.