Halak notched his 20th win of the season and lowered his goals-against average to 2.25 for the Blues, who won for just the second time in five games.
The Red Wings, losers of three of their last four games, got their only score from Gustav Nyquist.
Jimmy Howard yielded three goals on 25 shots before leaving in the second period with an undisclosed illness.
Peter Mrazek stopped 13-of-14 shots the rest of the way.
Notable deaths of 2014 [PHOTOS]
Julius Randle breaks leg during NBA debut