Match ends, Brighton and Hove Albion 0, Leicester City 2.
Brighton's loss to 10-man Leicester, with Glenn Murray missing a penalty, was "hard to take" said Chris Hughton.
Leicester scored twice and had Wilfred Ndidi sent off in the last few minutes, all after Brighton striker Glenn Murray had missed a penalty.
"It's frustrating and hard to take. It was certainly not a game that we deserved to lose," said Hughton.
The win keeps Leicester in eighth, while Brighton drop one place to 13th in the table.
Foxes keeper Kasper Schmeichel saved Murray's penalty in the 77th minute, with Vicente Iborra's header putting Leicester into the lead shortly afterwards.
Ndidi's foul on Shane Duffy earned the midfielder his second yellow card, but Leicester hung on with Jamie Vardy adding Leicester's second deep into injury time.
"The next bit is that we've got to score goals ourselves," Hughton added. "We created good opportunities and had decent chances to score.
"They got a lift in the last period of the game, following the penalty miss, and that got them the goal."
A quiet game had finally come alive when Ndidi fouled Jose Izquierdo in the Leicester area, but Murray's tame effort from the spot was parried away by Schmeichel, low to his left.
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Iborra rose to Ben Chilwell's cross from the left to place the ball beyond Brighton keeper Mathew Ryan and, after Ndidi's dismissal, Brighton defender Gaetan Bong missed at close range from a corner.
Vardy converted Demarai Gray's cross to ensure Leicester sealed their second consecutive away win in the Premier League.
Nightmare for Murray
This will be a game that Glenn Murray will want to forget about very quickly.
The Cumbrian striker's 11 league goals make him Brighton's leading scorer this season and it was a surprise to see him miss the target completely when one-on-one with Schmeichel shortly before half-time.
His spot kick lacked conviction and it proved to be the game's turning point, with the visitors making the most of the opportunity to snatch all three points.
Brighton are still six points above the relegation zone, and they now face fellow strugglers Huddersfield and Crystal Palace in their next two outings.
Murray will be hoping that a rare bad day at the office does not have more serious ramifications by the end of the season, when their last two games are at home to Manchester United and then away at Liverpool.
Gutsy Leicester hang on
With Leicester barely registering in attack, Schmeichel's contribution between the posts proved to be pivotal, both at the penalty and at a couple of other moments.
He pushed away a long-range shot from Pascal Gross early in the second half, and kept out Solly March just after Iborra had nodded the Foxes ahead.
Ndidi's clumsy contribution did not help Leicester's cause, but the steely resolve instilled by Claude Puel since he took over as manager in October helped the 2015-16 Premier League winners grind out the result.
Few would have predicted that Puel's side would be, just about, in the mix for a place in the Europa League at the end of the season when he replaced Craig Shakespeare.
But gritty displays like this, coupled with the excellent form of Vardy, mean that finishing sixth or seventh is not out of the question.
Man of the match - Kasper Schmeichel (Leicester City)
What the managers said
Brighton manager Chris Hughton: "We are hugely disappointed and it was a game we didn't deserve to lose. I thought the things we needed to do to nullify their strengths we did very well, but the next bit is scoring goals ourselves.
Asked whether the penalty miss changed the balance of the game, Hughton said: "They are the moments in a game we want to go our way but it doesn't and that gives them the advantage.
"It happens and Glenn [Murray] has scored penalties and vital goals for us this season. Leicester will be grateful for a good save and we are disappointed we missed it."
Leicester manager Claude Puel:
"I don't know if the result is fair but we take the three points and it's an important cushion for us.
"Brighton played well and they had quality so it was difficult for us in the first half after the international break. In the second half it was better and the penalty save from Kasper [Schmeichel] changed the situation. It gave us the belief to score both goals.
Asked whether Wilfred Ndidi's sending off was fair, Puel said: "I don't understand why he was sent off because when I watched the reply it wasn't a foul. He touched the ball and it changed direction.
"I hope it can be watched by the commissioner again because he is a crucial player for us."
Schmeichel equal with his dad - the stats you may have missed
- Kasper Schmeichel has saved three of the 14 Premier League penalties he's faced - the same number his father Peter saved during his time in the competition (21 faced).
- This was Brighton's fourth Premier League home defeat, and first against a non 'big-six' side.
- Wilfred Ndidi's red card was Leicester's fourth of the season in the Premier League - no side has been shown more (level with Chelsea and Watford).
- This was the 23rd away Premier League game in which Leicester had a player sent off, but only the second they went on to win (also beating Hull in December 2014).
- Jamie Vardy has scored in five of Leicester's last six away league games, with the other game in that run ending 0-0.
- Vicente Iborra has scored in back-to-back Premier League games, after netting in just one of his first 14 in the competition.
- Of Iborra's goals in the big five European leagues, 38% have been headers (12/32).
Brighton face a side three points and three places behind them when they take on Huddersfield Town on Saturday, 7 April at 15:00 BST. Leicester are also in action on 7 April, playing Newcastle at the King Power Stadium at 15:00 BST.
- 3BongBooked at 79mins
- 25LocadiaSubstituted forMarchat 75'minutes
- 7KayalBooked at 66minsSubstituted forBaldockat 84'minutes
- 2SimpsonBooked at 64mins
- 5MorganBooked at 12mins
- 15MaguireBooked at 68mins
- 3ChilwellBooked at 63mins
- 26MahrezSubstituted forFuchsat 85'minutes
- 25NdidiBooked at 87mins
- 11AlbrightonSubstituted forGrayat 79'minutes
- 20OkazakiSubstituted forDiabatéat 56'minutes
- 14Adrien Silva
- Chris Kavanagh
- Shots on Target
Second Half ends, Brighton and Hove Albion 0, Leicester City 2.
Goal! Brighton and Hove Albion 0, Leicester City 2. Jamie Vardy (Leicester City) left footed shot from very close range to the bottom left corner. Assisted by Demarai Gray following a fast break.
Corner, Brighton and Hove Albion. Conceded by Christian Fuchs.
Attempt missed. Glenn Murray (Brighton and Hove Albion) header from the centre of the box misses to the left. Assisted by Pascal Groß with a cross.
Corner, Brighton and Hove Albion. Conceded by Vicente Iborra.
Corner, Brighton and Hove Albion. Conceded by Ben Chilwell.
Corner, Brighton and Hove Albion. Conceded by Kasper Schmeichel.
Attempt saved. Solly March (Brighton and Hove Albion) left footed shot from outside the box is saved in the top centre of the goal.
Second yellow card to Wilfred Ndidi (Leicester City) for a bad foul.
Foul by Wilfred Ndidi (Leicester City).
Shane Duffy (Brighton and Hove Albion) wins a free kick in the attacking half.
Substitution, Leicester City. Christian Fuchs replaces Riyad Mahrez.
Substitution, Brighton and Hove Albion. Sam Baldock replaces Beram Kayal.
Goal! Brighton and Hove Albion 0, Leicester City 1. Vicente Iborra (Leicester City) header from the centre of the box to the bottom right corner. Assisted by Ben Chilwell with a cross following a set piece situation.
Riyad Mahrez (Leicester City) wins a free kick in the attacking half.
Foul by Beram Kayal (Brighton and Hove Albion).
Attempt missed. Wilfred Ndidi (Leicester City) right footed shot from outside the box is high and wide to the right following a corner.
Corner, Leicester City. Conceded by Gaëtan Bong.
Substitution, Leicester City. Demarai Gray replaces Marc Albrighton.