Robert Lang and Pavel Datsyuk also scored for Detroit, which has won five straight to pull to within a point of Central Division-leading Nashville. The Red Wings have won 11 in a row at home - matching their longest winning streak in three years - and are 20-3-3 overall at Joe Louis Arena.
Owen Nolan and Shane Doan scored for Phoenix, which has lost four of six games.
Detroit's Dominik Hasek made 20 saves.
Curtis Joseph stopped 44 shots to give the Coyotes a chance against one of his former teams.
Phoenix had a 4-on-3 power play with just under six minutes left, but failed to put much pressure on Hasek. Datsyuk scored into the empty net in the final minute to seal the win.