Dean Ashton opened the scoring on six minutes with a smartly-taken volley after a determined run from midfielder Andy Hughes supplied the striker with a pinpoint cross.
Both sides had failed to open their promotion campaigns with the best of starts; Norwich came into the game having drawn with Coventry City and Crewe Alexandra. Palace's new-term jitters were evident as they were soundly beaten at home by league newcomers Luton Town, before losing to Wolves midweek.
The home side's industry was to be undone minutes from the interval, however, as goalkeeper Robert Green's poor throw-out to Darren Huckerby saw the winger dispossessed before Crystal Palace burst forward. The full-back Emmerson Boyce crossed for Andy Johnson to tap past the Norwich keeper. On the balance of play, it was just reward for some impressive attacking play by the team from south London, according to Palace's assistant manager Neil McDonald.
"We have seen a 100 per cent improvement from the Luton game and must be pleased with the number of chances we have created," said McDonald.
"Obviously we're disappointed to have conceded early goals in the last two matches but we are pleased at how things are progressing and now need to build on this for a first win."
Huckerby, unperturbed by the error, was brimming with self-belief, his charges at the visitors' defence a constant threat all afternoon. His manager Nigel Worthington's hopes of an immediate return to the Premiership rely greatly on the former Coventry star.
Ashton's huge presence around the penalty area was a familiar sight for the Palace defence and on 64 minutes, he carved an outstanding opportunity, turning Fitz Hall before unleashing a strike that rattled the woodwork.
Johnson tested Green with seven minutes to go, but the England striker's volley was saved by his fellow national squad member.
The result, the third draw out of three since the start of the season, left Ashton in reflective mood: "I am always pleased to score a goal, no matter how it comes.
"But it has been a very frustrating start to the season and you can see the crowd are frustrated too. But we have brought in players and it will take a few games for them to settle."
Goals: Ashton (6) 1-0; Johnson (42) 1-1.
Norwich City (4-4-2): Green; Drury (Charlton, 46), Colin, Fleming, Shackell; Huckerby, Marney, Safri (Jarrett, 79), Hughes; Ashton, McKenzie (Thorne, 79). Substitutes not used: Ward (gk), McVeigh.
Crystal Palace (4-4-2): Kiraly; Ward, Boyce, Hall, Borrowdale; Soares, Kolkka (Butterfield, 75), Leigertwood, Watson; Johnson, Macken (Andrews, 34). Substitutes not used: Speroni (gk), Hudson, Popovic.
Referee: I Williamson (Berkshire).
Booked: Palace Boyce, Hall, Leigertwood.
Man of the match: Ashton.
Attendance: 25,102.Reuse content