Crystal Palace's last away goals came in a 2-1 win over Liverpool at Anfield under Sam Allardyce in April
Crystal Palace climbed out of the Premier League relegation zone as they outplayed Claude Puel's resurgent Leicester to seal a rare away win.
Christian Benteke cost Palace victory when he missed an injury-time penalty he was not supposed to take last weekend, but the striker redeemed himself with a first-half header from Andros Townsend's cross - his first goal of the campaign.
Palace had failed to score in their past 10 league away games, but Roy Hodgson's organised and adventurous team added a second before the break when Benteke's strong run and pass set up Wilfried Zaha for a brilliant individual finish.
Leicester only tested goalkeeper Julian Speroni when they rallied in the second half - the Argentine reacting superbly to reach Riyad Mahrez's angled low drive with a strong palm.
And any potential comeback was hamstrung when Wilfred Ndidi was sent off on his birthday less than a minute after Vicente Iborra's header was correctly disallowed for a foul.
Ndidi - who turns 21 today - was shown a second yellow card for simulation in the penalty box with just under half an hour to play.
Palace had a much more legitimate penalty shout when Benteke was crumpled in the area by Marc Albrighton's sliding tackle from behind, but the referee waved away appeals for a chance to add extra gloss on an impressive away performance.
Bakary Sako eventually provided it - tucking away Ruben Loftus-Cheek's pass across goal to round off a 94th-minute counter-attack.
The Foxes, who so impressively dismantled Puel's former club Southampton in midweek, remain eighth in the table, while Palace rise four places to 14th - though the teams below them are yet to play this weekend.
Palace finally find the net
Palace had taken 90 shots over 10 games without finding the net away from home in the league - their last away goals came in a 2-1 victory over Liverpool at Anfield under Sam Allardyce in April.
It was the longest such run since 1949-50 - when Manchester City went 12 top-flight matches without scoring away - and was broken by Benteke, who himself had failed to score from 28 attempts in his past 13 matches.
In truth, as 10-man Leicester poured forward in the game's closing stages, Palace - and Benteke in particular - could easily have scored more than three.
Another Benteke header was kept out by an acrobatic Kasper Schmeichel star-jump save at the far post, and the Belgium striker also saw a shot diverted just wide by Wes Morgan's last-ditch block.
But in the end, it didn't even matter that Townsend shot horribly over the bar after another late counter.
Hodgson took over with Palace without a goal or a point from their opening five league matches, but his side are now eight games unbeaten having not lost since a 1-0 defeat at Tottenham on 5 November.
It is their best run in the English top flight since a series of 12 games without defeat was ended in October 1990.
Foxes fail to fire
Only Manchester City and Burnley had won more points than Leicester's tally of 17 from Puel's first eight matches in charge - and the Foxes went into his ninth game having won each of their past four.
But while Palace looked dangerous every time they went forward - Zaha, Townsend, Loftus-Cheek and Yohan Cabaye all conspiring around target man Benteke - Leicester were easily snuffed out by the away side's aggressive defence.
The isolated Jamie Vardy was far from his waspish best, while Mahrez - a spectator in the first half - lost the ball in midfield five minutes before half-time to spark the move with which Palace doubled their lead.
Zaha, who had already threatened with several promising runs, expertly took Benteke's pass in his stride, regained his balance, slid past the covering Ben Chilwell with a stepover and fired the ball past Schmeichel.
It was a brilliant goal, but few would have anticipated the gulf between Leicester's sluggish showing on Saturday and Wednesday's 4-1 victory at Southampton.
Man of the match - Wilfried Zaha (Crystal Palace)
Since the start of last season, Wilfried Zaha has been directly involved in 20 Premier League goals, more than any other Crystal Palace player (11 goals, nine assists)
Unwelcome birthday cards - the stats
- Roy Hodgson has never lost a competitive match against Leicester as a manager (P5 W4 D1 L0).
- Ndidi became the fourth player to be sent off on his birthday in a Premier League game, after Dwight Gayle (17 October 2015 against West Ham), Gerry Taggart (18 October 1997 v West Ham) and Les Ferdinand (8 December 1993 against Liverpool).
- Palace have kept three straight away clean sheets in the Premier League for the first time.
- Since making his Premier League debut in September 2012, Benteke has scored 24 headed goals - only Arsenal striker Olivier Giroud (27) has netted more in the competition in this period.
Leicester host Manchester City in the Carabao Cup quarter-finals on Tuesday (19:45 GMT kicxk-off), before a home Premier League game against Manchester United on 23 December (19:45).
Crystal Palace's next match is away at Swansea in a 15:00 kick-off in the Premier League on Saturday....