Petr Mrazek stopped 16 shots for Detroit.
Okposo opened the scoring with 9:03 left in the first when he put a cross-crease pass into the empty-side of the net off the rush for his 12th goal.
Grabner got his fifth goal, with 4:53 remaining in the opening period, when his shot from the left circle deflected off the stick of Detroit defenceman Brendan Smith. Cizikas made it 3-0, with 3:05 left in the first period, when he put in a one-time shot from in front of the net. It was Cizikas' fourth goal.
The Islanders' John Tavares hit the post less than 30 seconds into the second period.
NOTES: Red Wings defenceman Jonathan Ericsson went to the dressing room during the second period with an upper-body injury and did not return. ... Petr Mrazek started in goal for Detroit after Jonas Gustavsson came up with a tender groin and sat out as a precaution. ... The Islanders hadn't played in Detroit in nearly three years. Their last game at Joe Louis Arena was Dec. 31, 2010. ... Red Wings' RW Gustav Nyquist returned after missing three games with a groin injury. ... New York LW Matt Martin is from Windsor, Ontario, which is across the Detroit River from Detroit. ... Detroit C Stephen Weiss had sports hernia surgery in Philadelphia on Monday morning. He is expected to miss 6-to-8 weeks and the Red Wings are aiming for him to be back after the Olympic break, which is Feb. 9-25. ... A power outage in downtown Detroit forced the Red Wings to have their pre-game skate on Monday morning in a partially-lighted Joe Louis Arena.