Fresh off his match-saving double at Everton on Monday night, Demba Ba marked his return to Newcastle's starting line-up with a neat finish through the legs of Norwich keeper John Ruddy inside 20 minutes after latching onto Hatem Ben Arfa's brilliant through ball with a splendid first touch.
Newcastle should have been two goals up if it wasn't for the misfiring Papiss Cisse, who has yet to score this season, with the striker loosely placing his spot kick well over the bar after Steve Morison had nudged Mike Williamson in the back in an aerial challenge.
In the second half, Magpies keeper Steve Harper did well to thwart an advancing Andrew Surman early in the second half before Ruddy got low to his left to keep out Ben Arfa's attempt from range in what were the only two chances of any real consequence.
In the end, Ba's first-half strike was enough for Alan Pardew's men to record their second victory of the campaign as Norwich remain winless under Chris Hughton to sit 17th.
Sports Direct Arena, Newcastle - 49,402
Yellow cards:NU - Cheik Tiote 89' NOR - Jonny Howson 87'