Dale Stephens fired a terrific opener for the Seagulls early in the second half, but Stephen Dobbie levelled impressively only four minutes later.
Blackpool, losers of 12 of their previous 15 away games, had an early opportunity when Stephens gave the ball away and Isaiah Osbourne had a left-foot shot turned round the post by Polish goalkeeper Tomasz Kuszczak.
Brighton striker Jesse Lingard, on loan from Manchester United, showed his pace with a strong run to the edge of the area and later put a right-foot shot wide following a neat back-heel by Stephens.
Stephens then tried his luck from the edge of the area and his low drive was taken by long-serving keeper Matt Gilks.
Andrew Halliday displayed fine defending for Blackpool for robbing the on-rushing Lingard after Kazenga LuaLua supplied a perfect cross-field pass midway through the half.
Brighton had a let-off when Dobbie released Halliday in a good position but his delivery across goal was poor.
The Seagulls, unbeaten in their previous five games, almost broke the deadlock when an excellent corner from Stephens was headed inches over by top-scorer Leonardo Ulloa five minutes before the break.
Dobbie wasted a glorious opportunity to put Pool ahead by dragging a left-foot shot wide after indecision at the back from Spanish defender Bruno Saltor.
However, Brighton caught Pool napping at the start of the second half, with Stephens curling in a beauty from the edge of the box to give them the lead.
The midfielder struck left-footed into the top corner after Ulloa chested down a cross by defender Stephen Ward.
Albion’s lead lasted only four minutes though, with former Brighton loan player Dobbie equalising from an unstoppable shot in the 50th minute. Dobbie found the top right-hand corner after a back-heel from Andy Keogh.
Brighton substitute Will Buckley unselfishly set up Keith Andrews on the edge of the box and his low shot flew wide of Gilks’ right-hand post.
Lingard was off target for the Seagulls after a short pass from LuaLua put him into a useful position.
Brighton, roared on by a crowd of 27,610, came close again when a deflected shot by Stephens flew wide after an assist by Ulloa.
Ulloa later set up Buckley in front of goal, but the substitute put his shot wastefully over as the two teams shared the points.