Vicente Iborra's header on 83 minutes and a Jamie Vardy second with the last kick of the game handed the Foxes all three points as they became just the fourth team - along with Manchester City, Liverpool and Chelsea - to win on the south coast this season.
The fact the opener came after the in-form Glenn Murray had just missed a second-half spot kick, made the defeat even tougher to take for the Seagulls, who had more than matched the former champions for the majority of the clash.
Leicester also held out the final few minutes with ten men after Wilfred Ndidi was shown a second yellow card.
But Albion failed to find a leveller despite a couple of decent chances, before the away side added a second on the breakaway deep into five minutes of added time.
Albion were bidding to make it four home Premier League victories in a row, while the Foxes came into the match having won just one of their last six on the road. Leicester had not kept a clean sheet in their last six matches, while Albion's last shut-out came in December away to Newcastle.
Chris Hughton handed Jurgen Locadia his first Premier League start, in for the suspended Anthony Knockaert, while Dale Stephens missed out as expected. That meant Beram Kayal partnered Davy Propper in central midfield.
The home side started well with plenty of possession and neat passing. There was some industrious stuff from Locadia, who between him and Glenn Murray were deputising on the right-hand side when defending in the early exchanges.
The Dutchman fell, rode a tackle and played neat one-two came to nothing, but he received the ball again, raced into the box, but his shot was blocked away.
The best chance came on 14 minutes when Murray set Locadia away on the right and his first-time low cross was just millimeters in front of the arriving Jose Izquierdo.
Chances continued to prove few and far between in what was, despite a lack of goalmouth action, a competitive half. The next real effort at goal saw Murray intercept a slack Harry Maguire pass and got the ball out of his feet just inside the box, but whipped the ball just over Kasper Schmeichel's crossbar.
Just two minutes later and Albion should have led. Murray was put away one on one, but with Schmeichel racing out to close the ball, the normally clinical striker put wide of the right-hand post.
Immediately at the other end, a subdued Riyad Mahrez had his first real involvement, cutting inside from the right flank, but his subsequent strike was comfortably saved by Maty Ryan at his near post.
Albion almost led within 60 seconds of the second half as Locadia let the ball roll across his body to Pascal Gross and the midfielder forced a diving save from Schmeichel from 25 yards out.
The visitors started to have a dominant spell of possession from then and Gaetan Bong put in a brave defensive header on the hour mark to clear Ben Chilwell's cross as Jamie Vardy was preparing to acrobatically meet it.
Maguire then brought down a breaking Ezequiel Schelotto on the right wing to pick up Leicester's fifth booking of the afternoon, meaning the whole of the back four were on cautions.
A Vardy flick from a Chilwell cross then skidded off the surface, but Ryan was down well to gather on the stretch as the Foxes continued to enjoy a good spell of pressure.
Albion looked to have been given the helping hand they needed after being awarded a penalty on 76 minutes. Great work by substitute Solly March played in Izquierdo and the wide man planted his foot and was bundled over by Wilfred Ndidi.
Referee Chris Kavanagh pointed immediately to the spot, but Murray checked his run-up and a diving Schmeichel guessed right and pushed away the spot kick.
That lifted the traveling fans and players and they took the led on 83 minutes as Iborra glanced home Chilwell's in-swinging cross.
To set up a grandstand finish Ndidi was shown a second yellow card for a foul on Duffy with three minutes left to play, giving Albion a free kick just outside the box - but March's dipping effort was pushed over.
In five minutes added time, Murray glanced a Gross cross wide of the far post and an unmarked Bong failed to put home a corner at the far post.
Albion were then caught high up the pitch and substitue Demarai Gray was put away in the area and he calmly teed-up Vardy to smash home and put an unreflective gloss on the scoreline.
Brighton: Ryan; Schelotto, Duffy, Dunk, Bong, Locadia (March 74), Kayal (Baldock 84), Propper, Izquierdo, Gross, Murray. Unused subs: Krul, Bruno, Hemed, Goldson, Suttner.
Leicester City: Schmeichel, Simpson, Morgan, Maguire, Chilwell, Albrighton (Gray 78), Ndidi, Iborra, Mahrez (Fuchs 85), Okazaki (Diabate 56), Vardy. Unused subs: JakupoviÄ‡, DragoviÄ‡, Silva, Iheanacho.
Attendance: 30, 629.