Puncheon’s 68th-minute strike, a curling effort from the right of the box beyond Canaries keeper John Ruddy, was the best moment of the match by far.
The first-half was full of effort but lacked quality as two sides haunted by the drop flailed at each other frantically.
Norwich felt they were denied a penalty when Matt Jarvis was barged over by Damien Delaney but the fourth-bottom Canaries should have tested jittery keeper Wayne Hennessey far more often.
Alex Neil’s side had hauled themselves out of the drop zone by beating West Brom and Newcastle.
And they know they have the chance to stop Sunderland overtaking them when the Black Cats come to Carrow Road on Saturday.
Midfielder Gary O’Neil said: “It was always going to be massive, we knew that the three games – Newcastle, Palace and Sunderland – were all going to be huge.
“We had a great response last week at home to Newcastle in a massive, massive game and we need the same again next week.”
Crystal Palace (4-2-3-1): Hennessey 5; Ward 7, Dann 7, Delaney 7, Souare 7; Jedinak 6, Cabaye 6; Bolasie 6, PUNCHEON 7 (Ledley 76), Sako 5 (Zaha 65, 7); Gayle 6 (Wickham 79).
Subs: Speroni, Campbell, Lee, Kelly.
Up Next: Everton (h), Premier League, Wednesday
Norwich City (4-4-1-1): Ruddy 6; Wisdom 6, Bennett 7, Klose 6 (Bassong 40, 6), Olsson 7; Jarvis 7 (Redmond 76), HOWSON 7, O’Neil 6, Brady 7; Naismith 5 (Bamford 66, 4); Mbokani 6.
Subs:Rudd, Jerome, Hoolahan, Mulumbu.
Up Next: Sunderland (h), Premier League, Saturday
Referee: Mike Oliver 7.
Star Player: Jason Puncheon – Vital winner.
Star Shocker: Wayne Hennessey – Kept dropping the ball.