Okposo got his first goal with 7:47 left in the final period to give the Islanders their first lead, and Minnesota's Justin Fontaine answered quickly to again knot it up.
But only 27 seconds later, the St. Paul, Minn., native batted in the rebound of a Thomas Vanek shot for the decisive blow.
Okposo also added an assist and Hickey set up two goals for the Islanders.
Kevin Poulin earned the win with 33 saves.
Nino Niederreiter had a goal and assist for the Wild, who dropped a fifth straight. Jonas Brodin and Ryan Suter also scored.
Josh Harding stopped 26-of-31 shots for Minnesota.