The Seagulls were ahead at the break after scoring with their only chance of the first half, but they struggled to cope when Pools came back in the second half.
The turning point was a controversial penalty that earned Hartlepool their equaliser, but over the 90 minutes they probably deserved the win.
The home team started with promise, Matty Robson's shot from the left well saved at the base of his right-hand post by Brighton keeper Michels Kuipers, who also did well to stop a low shot from David Foley.
But it was Brighton who took the lead, the busy Dean Cox sending Nicky Forster into the home area with a great pass and the striker went wide on the left to beat his man before finishing well from a tight angle.
As Hartlepool tried to come back, Kuipers flapped at a great left-wing cross from Robson under his own bar, but Matt Richards was at the far post to scramble the ball away.
Hartlepool gradually took control of the game in the second half and two goals in four minutes gave them the lead.
Kuipers had made good saves from Foley and Robson, but he couldn't stop Joel Porter's 66th minute penalty, after Porter was fouled by Colin Hawkins as they went for a high ball in the area, though Brighton felt the decision was a harsh one.
And on 70 minutes Gary Liddle scored with a low shot from the edge of the area following Antony Sweeney's right-wing cross.
Brighton had a Cox goal ruled out three minutes later ruled out for offside as they tried to stage a fightback of their own, but it ended in failure.