The Thrashers, losers of three straight, dropped to 9-14-2 at home. Only the Islanders' 19 points at home are fewer than Atlanta's 20.
Doug Weight's eighth goal chased Thrashers goalie Kari Lehtonen, who faced just 15 shots, just 13:17 into the game.
With 7:21 remaining, Okposo's ninth goal, a wrister from the bottom of the right circle, gave New York a 5-3 lead and helped Danis compose himself. It also made a tough-luck loser out of Johan Hedberg, who stopped 17 of 18 shots, but was saddled with the defeat since Okposo's second goal proved to be the difference.
Ilya Kovalchuk's 21st goal, a tip-in with 58 seconds remaining, ended the scoring. Each team gave up four goals in a period, Atlanta in the first and New York in the third.
Danis stopped the first 22 shots he faced before Zach Bogosian's slap shot - the rookie defenseman's third goal - cut the lead to 4-1 in the first minute of the third.
With 13:40 remaining, Atlanta's Rich Peverley made it 4-2 on the power play, using a backhander for his fifth goal. Marty Reasoner's wraparound made it 4-3 two minutes later.
Entering with an NHL-worst 12 points on the road, the Islanders hadn't won away from home since taking a shootout against the Canadiens on Nov. 24.
Trent Hunter, who missed two games due to a hand laceration, opened the scoring 55 seconds into the first. His wrist shot produced his 12th and first since a Dec. 4 loss at Washington.
Okposo, who has four goals in three games, made it 2-0. The NHL's seventh overall draft pick in 2006, Okposo scored on the power play in the previous two games.
Notes: New York, matching a season-high four goals in a period, also scored four during the first of a 5-2 win over St. Louis on Oct. 11. ... The Thrashers dropped to 3-1 against the Islanders this season.