The Foxes were indebted to Glenn Murray as he missed a 77th minute penalty. However, Vicente Iborra struck with a header in the 83rd minute before Jamie Vardy scored with the final kick of the game to make sure it was a huge missed opportunity for Brighton in their fight against relegation.
Wilfred N'didi was given his second yellow card of the season for two bookable offences and was given his marching orders in the 87th minute.
Brighton boss Chris Hughton made just one change to his Seagulls side that lost 2-0 to Manchester United in the FA Cup before the international break; Jurgen Locadia coming in for the suspended Anthony Knockaert for his first Premier League start.
Meanwhile, Claude Puel also made one change to his Leicester team. Shinji Okazaki came in for Kelechi Iheanacho, who broke his hand on international duty. The Nigerian however was fit enough for a place on the bench.
Tentative opening period
It was the hosts who had the better of the play in the opening 15 minutes. Locadia was first released down the left and tried a first-time volley from a tight angle but it was not able to trouble Kasper Schmeichel as the ball spun off of his shin and behind.
The Dutchman then produced a teasing low ball to José Izquierdo but the speedy wideman failed to apply a touch only yards from goal.
Iborra carved out the first opportunity for the visitors as he connected with Marc Albrighton's free-kick. Mat Ryan in the Brighton goal collected comfortably however.
Chances flow as the first-half comes to a close
Murray then collected a poor pass from Harry Maguire and attempted to beat Schmeichel with a speculative effort but the ball sailed over the crossbar.
The Brighton striker was also guilty of spurning the best opportunity of the opening half. Played through by an excellent through-ball from Pascal Groß, the 34-year-old looked sure to open the scoring but somehow curled his effort wide when one-on-one.
Riyad Mahrez then tested Ryan in the home side's goal barely a minute later. Finding space on the right side, the Algerian wriggled inside and aimed for the near post with a low effort. The Brighton stopper though held comfortably as the two sides went into the break level.
Promising second period from the Seagulls
The Seagulls started the second period on the front foot as Groß stole the ball away from Maguire. The German trotted forwards and tried to beat Schmeichel from distance but the goalkeeper palmed the ball behind for a corner.
The England defender redeemed himself however as Izquierdo raced away down the left side. The Colombian was tracked all the way and had his low shot blocked by the former Hull City man as he cut inside.
Murray pays the penalty for spot-kick miss
Hughton's men were given a wonderful opportunity to seize the lead with only 15 minutes remaining as they were awarded a penalty. Substitute Solly March released Izquierdo in the box with the Colombian attempting to wriggle in-between Maguire and Wilfred N'didi before falling due to a challenge from the latter.
The referee did not hesitate in pointing the spot with Murray stepping up. The frontman's effort from the spot was denied though as Schmeichel dived the correct way.
The scores did not stay level for much longer but it was the visitors who snatched the advantage through Iborra. Ben Chilwell found far too much space on the left and crossed towards the Spanish midfielder. He manufactured a few yards and nodded into the bottom corner with a deft header.
Vardy wraps up three points as Leicester go down to ten
There was to be late drama as Wilfred N'didi picked up his second yellow card and was given his marching orders. After picking up his first caution in the opening period, the Nigerian midfielder fouled Shane Duffy as the defender trotted forwards and was shown a red.
Consequently, Brighton continued to push in the closing stages but it would be Leicester who struck late to seal the three points. Demarai Gray, who had been introduced for Albrighton, sprinted down field and crossed to Jamie Vardy who was waiting unmarked at the far post. The England striker easily tapped home into the unguarded net to round off a fantastic victory for the Foxes.
As a result, Leicester stay in eighth, only three points behind Burnley in the Premier League table. Brighton meanwhile are 13th but only six points above the relegation zone.