Sutter scored with 43 seconds left in the first period on assists from Derek Joslin and Chad LaRose and Ward logged his third shutout of the year, blanking the Sabres on three power plays.
Carolina moved to within two points of Buffalo for the final Eastern Conference playoff spot.
Buffalo's Ryan Miller took the loss despite stopping 31-of-32 shots and stonewalling Carolina on all five of its power plays.
UPI Sports Results for September 20, 2014
UPI Sports Results for September 19, 2014