Brighton soaked up early home pressure, keeper Michael Kuipers saving well on his line from Matty Robson and David Foley as Hartlepool pressured for a breakthrough.
And the visitors got their reward after 28 minutes when they took the lead with their only real chance of the first half. Dean Cox's pass opened up the home defence for Nicky Forster to finish from a tight angle on the left of the area after going round his marker.
Hartlepool took over in the second half, and two goals in four minutes put them in command.
After 66 minutes Joel Porter levelled from the spot after being fouled in the area by Colin Hawkins, and then Antony Sweeney pulled a cross back from the right for Gary Liddle to slot a low shot into the bottom corner from the edge of the area.
But Brighton thought they were level again three minutes later when David Livermore crossed from the right and Cox slotted in, but an offside flag ruled it out.