Benteke, Wilfried Zaha and Bakary Sako all notched on the break at the King Power Stadium for the Eagles, who ended a run of 10 consecutive games without an away goal in the top flight in order to record their first win on the road since April.
Palace began the contest with renewed confidence following their midweek win over Watford, leaving Ruben Loftus-Cheek to test Kasper Schmeichel early on with a driven effort down low to the keeper's right.
The Eagles managed to setup in a system that effectively nullified much of Leicester's threat on the counter, allowing the visitors to find more time on the ball both in the middle and at the back.
Roy Hodgson's tactical decisions soon proved decisive when the ball was moved out from the middle into the path of Andros Townsend, who turned a curling ball into the box towards Benteke, who snuck between Danny Simpson and Wes Morgan to head beyond Schmeichel and end his drought.
If Leicester were to find a route back into the contest it was likely to come through Demarai Gray down the left flank, the youngster driving well to find Vardy in the box, who then slipped at the vital moment before testing Julian Speroni.
Benteke's newfound confidence soon led to Palace's second of the afternoon, as the striker burst forward beyond two markers to feed a pass on the overlap to Zaha, leaving the winger time to produce a step-over to fool his marker and lash down low past Schmeichel.
The visitors continued to show promise on the break in the second half, as James McArthur won back possession before feeding Townsend, but Benteke could not find the quality to convert his diving header at the near post.
The hosts thought that they had broken Palace's resolve after the hour mark, however Vicente Iborra's headed effort was chalked off after the referee spotted an infringement from the Spaniard on James Tomkins inside the box.
The promise of a Foxes comeback was arguably quashed with just under 30 minutes to play when Wilfred Ndidi was shown a second yellow for a dive on his birthday, leaving Claude Puel quietly seething on the touchline.
Benteke might have returned to bag his second of the afternoon but he was denied by Schmeichel at point-blank range, although the home stopper was later beaten by an injury-time curling effort from substitute Sako, who condemned the hosts to a humbling 3-0 defeat.
Palace have now put together their longest undefeated run in the top flight of English football since a streak of 12 games in 1990, while Hodgson's side have achieved seven straight games unbeaten in the Premier League for the first time in the club's history.
Leicester City (4-5-1): Schmeichel; Simpson, Morgan, Maguire, Chilwell; Iborra (Okazaki 77'), Ndidi, Mahrez, Albrighton (King 77'), Gray; Vardy (Ulloa 85')
Crystal Palace (4-3-3): Speroni; Kelly, Tomkins, Dann, Schlupp; McArthur, Cabaye (Riedewald 85'), Loftus-Cheek; Townsend, Zaha, Benteke (Sako 88')