The Islanders snapped a three-game losing streak and handed the Oilers their fifth consecutive defeat. Four of Edmonton's seven setbacks this year have come by a single goal.
Edmonton took a 2-1 lead into the second period, but Okposo tied it on the power play 4:54 into the stanza and Tavares scored what turned out to be the winning goal with 1:17 left.
Evegeni Nabokov gave up two goals to Taylor Hall 8 seconds apart late in the first period, but turned aside the other 29 shots he saw to pick up the victory.
Josh Bailey opened the scoring for New York 9:59 into the contest, but the Oilers grabbed the lead on the quick back-to-back goals from Hall, his second and third of the season.
The loss went to Devan Dubnyk, who made 36 saves.