Ben Watson, who set up the first, made it 2-0 with a shot from the edge of the box and Clinton Morrison finished off Tom Soares' approach work for 3-0.
Watson was involved again in the fourth as he supplied the cross for Fitz Hall to head home.
Darren Ward put Darren Huckerby's cross into his own net but it was of little consolation to an uninspired Norwich.
Norwich manager Nigel Worthington:
"Crystal Palace were very good but we were less than average. It is disappointing.
"We have been on a nice run and we didn't do the things behind it. Between Palace doing well and us not turning up, it was one-way traffic.
"If you haven't got the ball you can't play football. Every time we got the ball we gave it straight back to them."
Crystal Palace: Kiraly, Ward, Borrowdale, Boyce, Fitz Hall, McAnuff (Andrews 64), Watson, Hughes, Soares (Leigertwood 74), Johnson (Freedman 81), Morrison.
Subs Not Used: Popovic, Speroni.
Booked: Andrews.
Goals: Johnson 7, Watson 34, Morrison 54, Fitz Hall 62.
Norwich: Green, Drury, Fleming, Doherty, Rehman, Safri (Etuhu 44), Robinson, Huckerby, Johansson (McVeigh 45), Thorne (McKenzie 57), Earnshaw.
Subs Not Used: Gallacher, Colin.
Booked: Doherty.
Goals: Ward 88 og.
Att: 19,066
Ref: P Walton (Northamptonshire).