Shorthanded success stops Wings' slide
Dominik Hasek made 20 saves for the Red Wings, who broke a five-game winless streak (0-2-3).
Antti Miettinen scored for Dallas, which had its three-game winning streak snapped.
Schneider broke a 1-1 tie with 7:47 remaining with teammate Dan Cleary off for holding.
After taking a pass from Henrik Zetterberg, Schneider blasted a slap shot past Marty Turco from the high slot for his sixth goal.
Draper got the Wings even at 1 at 3:03 of the third period with Jiri Hudler in the penalty box for tripping. He put the carom of Nicklas Lidstrom's shot off the back boards between Turco's pads
Turco, who made 27 saves, fell to 1-8-5 against the Wings.
Dallas opened the scoring 6:22 into the second period, when Miettinen beat Hasek with a one-timer from along the goal line below the left circle. He took a pass from Mike Ribeiro, who was in the high slot, after a turnover by Detroit's Jason Williams.
Dallas was 0-for-5 on the power play, while allowing two goals against. The Wings went 0-for-2 when they had the advantage.
Notes: Williams was helped off the ice as he favored his right leg after a hit by Dallas' Niklas Hagman late in the second period. Williams was playing his fifth game after missing three following a concussion. ... Red Wings LW Johan Franzen missed his third game because of a concussion and sore knee. ... Dallas captain Brenden Morrow didn't play because of a groin strain.