The Hurricanes moved within two points of the eighth-place New York Rangers for the final playoff berth in the Eastern Conference. Both teams have two games remaining.
Ward has 16 shutouts in his six-year career, all of it spent with Carolina. His largest single-season shutout total has been six, recorded in 2008-09.
Derek Joslin and Jeff Skinner scored in the second period and Erik Cole added some insurance early in the third.
Jimmy Howard gave up all three goals on 32 shots for Detroit, which wrapped up the Central Division title last weekend.
Ward won for the first time in his career against the Red Wings. He had lost in his three previous appearances against them.