Kaoru Mitoma sent the Seagulls ahead in the 27th minute, but Marc Albrighton levelled the scores before Harvey Barnes struck for Brendan Rodgers's side just past the hour.
Brighton refused to be beaten, though, and Ferguson headed a late equaliser to secure a point for Roberto De Zerbi's side, who have moved into sixth position in the Premier League table.
Leicester, meanwhile, sit 14th, moving onto 18 points from their 20 league games this term, with the draw ending a run of four straight losses in England's top flight.
The first serious opening of the match came in the 24th minute when Pascal Gross's corner caused problems inside the Leicester box, but Jan Paul van Hecke's header was just too high.
Brighton managed to take the lead in the 27th minute, though, with Mitoma working his way towards the edge of the Leicester penalty area before curling an unstoppable effort into the far corner of the net.
The Foxes answered back before the break, with Albrighton, who had only entered the field as a substitute in the 35th minute, levelling the scores in the 38th minute.
Brighton failed to clear inside their own penalty box, and the ball eventually broke for Albrighton, with the attacker managing to squeeze the ball under the advancing Robert Sanchez; VAR checked for a possible offside on Barnes, but the goal stood, and the two teams were level at the half-time break.
The away side had a huge shout for a penalty early in the second period when Danny Welbeck was challenged by Luke Thomas, but the referee was not interested and VAR agreed with what was a very controversial decision.
Brighton had a golden chance to regain the lead just before the hour when Mitoma found Solly March inside the box, but the attacker fired his effort over the crossbar.
It was Leicester that scored the game's third goal in the 63rd minute, though, with Barnes firing home at the far post after Thomas had flicked an Albrighton corner towards his teammate.
Danny Ward did brilliantly to keep out a strike from March in the 76th minute, as Brighton looked for a leveller, and it eventually came in the 88th minute when Ferguson headed a cross from Pervis Estupinan into the back of the net off the post.
James Maddison had the chance to win it for Leicester late on, but the England international's free kick missed the target, with the two teams being forced to settle for a share of the spoils.
Next up for Leicester is a trip to Walsall in the FA Cup next Saturday, while Brighton will take on Liverpool in the same competition next Sunday.