Henrik Lundqvist made 26 saves to add to the recent struggles for the Red Wings, who have lost six in a row. Detroit has a 2-7-1 record this month and began the night with a two-point lead over Chicago for home-ice advantage in the first round of the playoffs.
The Red Wings are second to Chicago in most goals in the Western Conference, but they could manage only a first-period score from Henrik Zetterberg.
Lundqvist shut out Detroit for the game's final 56:24. The Rangers moved three points in front of idle Pittsburgh for the best record in the Eastern Conference.
Conklin made 32 saves while filling in for Jimmy Howard, who missed the game with a groin injury.