The Islanders were trailing 2-1 with 4:16 remaining in the third when Okposo launched a wrist shot from above the right circle that rattled off two pipes and went behind Dan Ellis for the equalizer -- his second goal of the game.
Then with 1:24 left, Calvin de Haan broke into the Stars zone and sent a pass through the crease to Tavares, who was alone at the side of the net to put in his 21st of the season for the decisive score.
Tavares also had an assist, de Haan finished with two assists and Brock Nelson added an empty-netter for the Isles, who won a fourth straight and seventh in eight overall.
Kevin Poulin stopped 29-of-31 shots for the victory.
Ellis ended with 27 saves.