Cisse struck in the 11th minute for his third goal in matches at St. James Park, slipping past Norwich defender Zak Whitbread to redirect Jonas Gutierrez's cross past goalkeeper John Ruddy.
Newcastle is five points from the fourth and final qualifying spot for the Champions League, although Arsenal has a match in hand.
Ruddy made several saves to keep Norwich in the match, while Newcastle goalkeeper Tim Krul made late stops to deny Anthony Pilkington and Whitbread.
Norwich is in 13th place, 13 points below fifth-place Chelsea in the final European qualifying spot and 14 above the drop zone.