Burnley opened the scoring when Ade Akinbiyi angled his header past the goalkeeper from Dean Bowditch's cross.
The Clarets could have wrapped up the game before half-time but Hammond converted Paul Reid's cross from the right to earn Brighton a point.
Brighton boss Mark McGhee:
"We felt that unless we won we would stay in the bottom three.
"The important thing was to take something out of the game. If we win one game, I think we will stay up.
"I had a bit of a rant at half-time at one or two as we didn't get close enough to them, but we changed to a 4-4-2 and were unlucky not to win."
Burnley: Coyne, Duff (Roche 75), McGreal, Cahill, Camara, O'Connor, Grant, Hyde, Branch, Akinbiyi, Bowditch.
Subs Not Used: Oster, Jensen, Pilkington, Valois.
Booked: Cahill.
Goals: Akinbiyi 23.
Brighton: Blayney, Virgo, El-Abd, Butters, Reid, Harding, Carpenter, Oatway, Hammond, McCammon (Robinson 45), McPhee.
Subs Not Used: Mayo, Dolan, Nicolas, Shaaban.
Booked: Reid.
Goals: Hammond 52.
Att: 11,611
Ref: S Mathieson (Cheshire).