The Eagles were in stunning form throughout the afternoon and first-half strikes from Wilfried Zaha and James McArthur got them off to the perfect start.
Marc Albrighton was shown a straight red card for a professional foul mid-way through the second period. Goals from Ruben Loftus-Cheek, Patrick van Aanholt and a late penalty from Christian Benteke ensured the Eagles are now all-but safe in the top-flight of English football.
Roy Hodgson named an unchanged line-up for the third consecutive game at Selhurst Park. Zaha partnered Andros Townsend up-front in a fierce attacking duo.
Meanwhile, the under-pressure Claude Puel made two changes to his Leicester team. Foxes' captain Wes Morgan was recalled back into the line-up for Aleksandar Dragović. Youngster Hamza Choudhury also returned to the team as he replaced Adrien Silva.
Close escapes but Zaha snatches the lead
It was the hosts who enjoyed the better start as Kelechi Iheanacho had to make an important stop on the goal-line. Ben Hamer made a poor clearance from a corner and James Tomkins looked to be heading home from only a few yards out. Iheanacho though anticipated well to clear to the relief of his Foxes' teammates.
Joel Ward then had to be alert to make an excellent clearance of his own. Iheanacho played through Jamie Vardy with the Englishman's shot beating Wayne Hennessey. The defender however got back on the goal line though to clear.
Palace hit the front not long after through Zaha and it was an excellent move that earned the hosts the lead. Sumptuous inter-play between Loftus-Cheek, Yohan Cabaye and McArthur allowed Zaha to get free at the back post. He then powered a shot into the top corner beyond a helpless Hamer.
Eagles soar into the break
The winger could well have got a second had it not been for a clever stop after he found space in the area and tried to poke into the far corner but the Leicester stopper got down well to palm the ball behind.
Hodgson's men did eventually have their second however and Zaha was again key. He found McArthur with an excellent pass along the face of goal. The Scottish midfielder then turned cleverly and squeezed a low shot into the bottom corner to send the Eagles into the break with an excellent advantage.
Time for change, elects Puel
As a result of their wretched first-half, the visitors made two changes at the break. Silva and Fousseni Diabate replaced Choudhury and Iheanacho respectively. The Foxes were also forced into another change as Wilfred N'didi was withdrawn with an injury and was replaced by Dragović only minutes after the restart.
Leicester's afternoon got even worse as Marc Albrighton was given his marching orders. Chasing a long clearance, he hauled down Zaha who had quickly chased him down and looked to be winning the ball. Being the last man, he was then quickly shown the red card by Mike Dean.
The chances continued to flow for the hosts but Dragović intercepted well as Zaha attempted to pick out Loftus-Cheek when two-on-one. McArthur then had a brilliant opportunity to double his afternoon's tally but could only lift the ball wide from close range.
Palace close out brilliant win with two late goals
The hosts continued to exploit their man advantage though and Townsend could well have rounded off the scoring. His deflected shot just bobbled wide off the post however.
Palace did notch their third eventually and it was another excellently constructed strike. Mamadou Sakho moved into considerable space and played an excellent through-ball to Loftus-Cheek. The on-loan Chelsea man rounded Hamer and tapped home into the empty net.
It got even better in the closing stages as Patrick van Aanholt scored. Former Leicester wideman Jeffrey Schlupp should have netted only minutes after being introduced from the substitutes bench but Hamer did well to save. The deflection fell to van Aanholt who curled into the unguarded net.
Benteke was introduced as a substitute late in the day but still had time to make an impact as he was fouled in the penalty area by Harry Maguire. The Belgian stepped up to the spot and rolled the ball home to round off the scoring on a memorable evening for Hodgson's troops.
The Eagles are now six points clear of the relegation zone with two games left to go and now look pretty secure in their place in the Premier League next season. Meanwhile, Leicester's poor run under Puel continues ahead of their clash with West Ham United next week.