After going into the break 2-0 down, teenage substitute Michael Olise pulled a goal back for Palace with a brilliant volley past Kasper Schmeichel.
Former Leicester player Jeffrey Schlupp added a second just 48 seconds after his introduction, heading past Schmeichel with only his second touch.
Brendan Rodgers’ side opened the scoring against the run of play when Kelechi Iheanacho capitalised on a mistake from Joachim Andersen before slotting past Vicente Guaita on 31 minutes.
Jamie Vardy added a second six minutes later with a cool finish from Harvey Barnes’ assist.
The draw means Palace remain unbeaten at Selhurst Park under manager Patrick Vieira, who is the first Eagles manager to avoid defeat in his first four Premier League home games.
It is the first time since October 2003 that Leicester have failed to win a Premier League game in which they were leading by two or more goals at half-time as their winless run in the competition is extended to four matches.
Subs save the day for Palace
After conceding a 95th-minute equaliser against rivals Brighton on Monday night, Palace looked set to bounce back and had the best of the early chances as they dominated possession.The Eagles had two early shots on target in quick succession, but Schmeichel did well to deny Wilfried Zaha and Conor Gallagher, before the hosts were stunned by Iheanacho’s opener.
Against the run of play, Iheanacho – celebrating his 25th birthday – nicked the ball off Andersen and kept his cool before rolling past Guaita for his first Premier League goal of the season.
Six minutes later, Barnes had options both sides, with Iheanacho to his right and Vardy to his left. He opted for Vardy, who took a touch before side-footing in Leicester’s second.
The 34-year-old is now the Premier League’s leading goalscorer with six goals in seven games this season. Since turning 30, he has scored 90 goals in the competition.
Palace impressed early in the second half and went close through Odsonne Edouard, who crashed his effort against the crossbar after cutting inside Caglar Soyuncu and Jannik Vestergaard.
They finally find a breakthrough when, after replacing Jordan Ayew early in the second half, 19-year-old Olise saw his first effort from Tyrick Mitchell’s cross blocked, before he brilliantly volleyed the rebound past Schmeichel.
Aged 19 years and 295 days, Olise is the first teenager to score for Palace in the Premier League since Clinton Morrison in May 1998.
That goal really lifted the home crowd and it seemed like one-way traffic. Vieira got his substitutions spot on and Selhurst Park was sent into raptures when Schlupp headed in the equaliser against his former side.
His goal after 48 seconds is the second-quickest by a substitute in the Premier League this season, after team-mate Edouard took just 29 seconds to score against Tottenham.
Schlupp came close to heading in a second three minutes from time, but his effort glanced just wide of the far post as the sides were forced to settle for a point.