Anisimov was on his back, motionless, early in the second period after Quincey appeared to hit him in the head with his left fist and forearm.
The medical staff for both teams helped put Anisimov on a backboard before he was taken off the ice.
Anisimov was skating toward the back of the net alongside Detroit's Ian White when Anisimov lost his balance. Quincey landed a blow to Anisimov's head that didn't seem intentional.
The Joe Louis Arena crowd was quiet while Anisimov was being prepared to be put on a stretcher. Anisimov was cheered when he was wheeled off the ice.