Bradley Johnson, signed on loan from Leeds, made a dream debut with two goals, before an own goal by Jack Hobbs late on completed the turnaround.
It looked like plain sailing for Leicester in the first half as Matty Fryatt fired them into a 2-0 lead.
The former Walsall marksman opened the scoring in the 34th minute with an instant shot after Brighton skipper Steven Thomson cleared a cross from Max Gradel straight to him.
Fryatt pounced again for his 11th of the season seven minutes later, converting Gradel's volley at the far post from a cross by Lloyd Dyer from close range.
Brighton keeper John Sullivan, making his debut in place of Michel Kuipers, kept his team in the game on the stroke of half-time by parrying a shot from Andy King.
Brighton boss Micky Adams made a double substitution at half-time against his old club, bringing on Kevin Thornton and Dean Cox for Robbie Savage and Kevin McLeod.
It paid off handsomely, but only after Brighton survived strong appeals for a penalty when Fryatt was appeared to be brought down by Sullivan.
Thornton set up Johnson for a low left-foot drive which halved the arrears.
Johnson equalised with an even better strike from 25 yards six minutes from time and Brighton's recovery was complete when Hobbs diverted a cross from Joe Anyinsah into his own net.
Brighton's former Leicester boss Adams is still backing his old club to go up, saying: "They have got a strong squad and they will do well this season. I think they will achieve their goal of promotion if they just keep their heads."