At the King Power Stadium, Leicester went ahead five minutes into the second half thanks to a mistake from Palace keeper Vicente Guaita.
Marc Albrighton and Ayoze Perez combined to pick out Youri Tielemans and when the Belgian swung a cross into the six-yard box, Kelechi Iheanacho poked home after Guaita failed to collect.
Jamie Vardy bagged his 100th Premier League goal in the 77th minute, the striker becoming the 29th player to reach the milestone as he tapped in Harvey Barnes' pass.
Vardy struck again in the 90th minute as Leicester won for the first time in five games.
Norwich manager Daniel Farke conceded his side are heading for relegation after Leandro Trossard fired Brighton to a 1-0 win at Carrow Road.
Trossard netted in the first half to move Brighton nine points clear of the relegation zone before the bulk of the weekend's matches.
Brighton's second win in four games since the restart puts them in position beat the drop, but the picture is much bleaker for Norwich.
With five matches left, Norwich are seven points from safety after losing all five games following the coronavirus hiatus.
Farke knows Norwich's chances of avoiding an immediate return to the Championship are almost over, especially with games against Chelsea and Manchester City still to come.
"It was more or less our last chance to get back in the mix and we are disappointed," he said.
"After a few losses, we don't have the right to make any fighting messages or to make any unrealistic claims."