Depleted by a series of injuries to key players, Leicester has looked fatigued in recent weeks and fell behind after 10 minutes when Adam Lallana swept home his first goal for the Seagulls.
Brighton has made a habit of dominating games without making it count and once again paid for failing to build on its lead as Lallana struck the woodwork and Neal Maupay had a goal ruled out for offside.
Leicester looked lifeless for the first 45 minutes without James Maddison and Harvey Barnes, but bounced back after the break for a first win in four games.
Youri Tielemans's brilliant pass unlocked the home defence for Kelechi Iheanacho to coolly dink home the equaliser on 62 minutes.
Kasper Schmeichel then denied Lallana again with a fine save before a goalkeeping error at the other end handed Brendan Rodgers's men a vital victory.
Robert Sanchez flapped at Marc Albrighton's corner and Daniel Amartey headed into the unguarded net.
Leicester now has a seven-point cushion over fifth-placed Everton as it aims not to make the same mistake as last season when it crashed out of the top four at the business end of the campaign.
A fifth game without a win leaves Brighton still just three points above the relegation zone.