The Islanders built a four-goal lead before fighting off a comeback by the Thrashers. New York had lost 14 consecutive road contests, having last won away from home Nov. 24 in Montreal.
It was New York's second straight victory after losing eight straight.
New York led 4-0 after one period on goals by Trent Hunter, Okposo, Tim Jackman and Doug Weight -- all of the scores coming at even strength.
After a scoreless second period, Atlanta tallied three times in the first 8:36 of the third to make a game of it. Okposo then restored a two-goal advantage for the Islanders by beating Johan Hedberg on a wrist shot with 7:21 to play.
Ilya Kovalchuk again brought Atlanta within a goal with 52 seconds remaining, but Yann Danis held on down the stretch to complete a 33-save performance.
Atlanta lost its third straight. Hedberg replaced Kari Lehtonen after he had allowed four goals on 15 shots.
The Islanders were able to avoid equaling the longest road losing streak in franchise history. They dropped 15 in a row on the road in 1973.