Justin Abdelkader had a goal and an assist and Valtteri Filppula and Brett Lebda scored for Detroit (2-0), which got all of its goals in the third period. Starting goalie Chris Osgood made 18 saves and Thomas McCollum stopped 10 shots.
Williams broke the 2-2 tie with a slap shot from the top of the right circle that bet Zaba high on the long side. Abdelkader added his goal with 3:42 left.
Callahan pulled the Rangers within one with 2 minutes remaining.
The Red Wings scored twice in the first 1:23 of the third period to tie it at 2.
Filppula put Detroit on the board 30 seconds into the period when he beat Zaba with a wrist shot from the left circle. Lebda tied it 53 seconds later when his shot from a bad angle in the left wing corner found its way through Zaba on the short side.
Anisimov opened the scoring 7:26 into the first period when he beat Osgood with a wrist shot from the slot off the rush that was screened by Lebda.
Lisin made it 2-0 3:39 into the second period when he put in the rebound of Anisimov's shot.