Luka Milivojevic scored on his 100th Crystal Palace appearance as Norwich were beaten 2-0 at Selhurst Park.
Eagles captain Milivojevic scored his first goal of the season from the penalty spot after James McArthur was brought down in the area by Canaries defender Ibrahim Amadou in the first half, before Andros Townsend sealed the win with a second in stoppage-time.
Norwich had more possession and registered as many shots on target as Palace but Daniel Farke's side rarely threatened and lacked the clinical edge needed to avoid back-to-back away defeats.
Palace climb to ninth in the Premier League as a result of their third victory of the season, while Norwich drop to 17th, a point and a place above the relegation zone.
How Milivojevic marked Palace century
Palace nearly made a dream start inside two minutes as a high press presented Wilfried Zaha with the chance to open his account for the season, but the Ivorian blazed over.
Zaha turned provider on 13 minutes, slipping Jordan Ayew into a scoring position, but stand-in Norwich goalkeeper Ralf Fahrmann parried his shot away.
Palace were given the chance to open the scoring on 21 minutes when Amadou clumsily bundled McArthur over in the box. Penalty-specialist Milivojevic made no mistake from 12 yards, rifling the ball into the top corner past Fahrmann, whose final act was to pick the ball out of his own net before injury forced him off, with Michael McGovern replacing him.
Norwich tried to mount a revival before the interval but two saves in quick succession from Vicente Guaita to deny Teemu Pukki and Emu Buendia, either side of Martin Kelly clearing a Todd Cantwell shot off the line, kept the Canaries at bay.
Palace were quite content sitting back and defending their lead early in the second period, but with their narrow advantage encouraging Norwich, a second was needed.
Zaha nearly delivered just that on 83 minutes as he lost his marker to get on the end of Townsend's cross, but his header flashed over with the goal gaping.
But Zaha turned provider in time added on, holding up the ball on the edge of the box before rolling it into the path of Townsend, who sealed the victory with a clinical finish into the bottom corner.
What the managers said…
Crystal Palace manager Roy Hodgson: "We started brilliantly and really looked like taking the game by the scruff of the neck. Norwich came back at us, they are a good team, but we tightened up in the second half and got the balance right. I thought we would put the game to bed a little bit earlier but that last pass evaded us until Andros did just that."
Norwich head coach Daniel Farke: "Although we have a difficult situation in terms of injury, and the game started pretty unlucky with injury to our goalkeeper, we wanted to return with points, so we are disappointed. But I'm not interested in talking about our injuries, I'm more concerned with how we gain more points. We created many good scoring chances, especially in the first half, and should have scored and rewarded ourselves with a goal, then there would have been a big chance to win the game."
Opta stats
- Crystal Palace are unbeaten in their last six home Premier League games (W3 D3), their longest such run at Selhurst Park since April 1993 (W2 D4).
- Norwich are winless in 20 away Premier League games in London (D6 L14), the longest such run in the competition since Leicester between November 2000-March 2015 (D3 L17).
- Crystal Palace midfielder Luka Milivojevic's goal was his 25th in the Premier League, with 20 of those coming from the spot - making him the 12th player to score as many as 20 penalty goals in the competition.
What's next?
Palace travel to West Ham on Saturday Night Football, live on Sky Sports Premier League from 5pm; Kick-off 5.30pm. Norwich host Aston Villa at Carrow Road in the Premier League on Saturday at 3pm.