Palace had lost nine of their last 14 games – and six straight at home – but Puncheon’s curling effort surely means the Eagles, 16th on 37 points, are clear of relegation danger.
It is 20 years in May since Norwich last won at Palace – six draws in 14 matches – and their failure to get a point meant Aston Villa survived for another day.
The loss also means Alex Neil’s 17th-placed side can still join Villa in being demoted, piling more importance on next Saturday’s clash with Sunderland.
The Black Cats are four points behind Norwich, but have two games in hand, the first against leaders Leicester on Sunday.
Alan Pardew’s men, meanwhile, can face Everton on Wednesday with their top-flight status all-but mathematically certain after their first win in almost four months.
Norwich, who had beaten West Brom and Newcastle in successive games, may feel aggrieved after a first-half challenge from Damien Delaney on Matt Jarvis.
They appealed in vain for a penalty, but the fact referee Michael Oliver’s decision was a key talking point only showed the poor quality of the contest, even if it was settled by a fine goal.