Bailey had the first five-point night by an Islander at the Nassau Coliseum in more than 15 years and Okposo scored twice to reach the 20-goal mark for the first time in his career as New York completed a home-and-home sweep of Pittsburgh by beating the Penguins 5-3.
No Islander had scored five points in a home game since Niklas Andersson did it on Dec. 10, 1996.
"It's always sweeter to get them when you win," said Bailey, the ninth player taken in the 2008 NHL Draft, when asked about the biggest game of his four-year NHL career. "We did a lot of little things right, played good defense and found a way to score some goals. That's a recipe for winning."
The second loss in three nights to the last-place team in the Atlantic Division dealt another blow to the Penguins' hopes of catching the New York Rangers for first place in the division and the Eastern Conference. Pittsburgh now trails the Rangers by five points; each team has five games remaining.
Al Montoya, the likely starter for the rest of the season with Evgeni Nabokov sidelined by a lower-body injury, made 26 saves.
For the second straight game, the Islanders held Sidney Crosby off the scoresheet. Crosby left the game early in the second period when defenseman Dylan Reese's clearing pass hit him in the face. He left a bloody trail on the ice before being helped to the dressing room, but missed only about eight minutes of playing time before returning.
The Islanders, who won their third in a row, scored 10 goals in the back-to-back wins against the Penguins without a point from their top line of John Tavares, Matt Moulson and PA Parenteau.
"The wins that we've had recently, it's been the secondary scoring," coach Jack Capuano said. "It's good to see some of the guys who struggled earlier in the year are scoring some goals for us."
The recently formed trio of Bailey, Okposo and Frans Nielsen has more than picked up the slack.
"The three of us seem to mesh pretty well together," Bailey said. "It's worked well for a short period of time, and we want to finish the season that way."
Okposo extended his goal-scoring streak to four games and put the Islanders ahead to stay at 16:36 of the second period when his pass to the front of the net deflected off the skate of Pittsburgh defenseman Deryk Engelland for a power-play goal and a 2-1 lead. Bailey made it 3-1 two minutes later when he slid a breakaway backhander past Marc-Andre Fleury for a shorthanded goal.
Okposo reached the 20-goal mark at 5:52 of the third period when he slammed home a perfect feed from Bailey for a 4-1 lead.
"They’re pretty opportunistic," Fleury said. "Sometimes we controlled the play very well, then they’d come down in our zone. They have a good group of forwards and they’re dangerous around the net making those little plays in front. They got a few (goals) like that tonight."
Goals by Jordan Staal at 8:20 and Evgeni Malkin at 18:29 cut the Isles' lead to one, but Bailey iced the win by taking the puck away at his own blue line and hitting the empty net with 4.7 seconds remaining.
Bailey had three assists in the Isles' 5-3 win at Pittsburgh on Tuesday, giving him eight points in two games.
The Islanders, now 5-1-0 in their last six, swept a home-and-home series against the Penguins for the first time since November 1986.
"We have a young team and guys are learning how to win every day," said 39-year-old Isles forward Jay Pandolfo, who set up Bailey's shorthanded goal with a spectacular diving play. "It's good to see."
New York opened the scoring at 11:07 of the first period when Marty Reasoner scored for the first time in 71 games dating to March 8, 2011, when he was a member of the Florida Panthers. Reasoner, a free-agent signing by the Isles last summer, raced down the slot and whipped a perfect feed by Mark Streit past Fleury.
Pittsburgh tied it 8:37 into the second period on a shorthanded goal by Pascal Dupuis, who outworked Streit in the Isles' zone and snapped a shot from the left circle past Al Montoya.
Malkin, the NHL scoring leader, became the first player this season to reach the 100-point mark when he scored from the slot with Fleury on the bench for a sixth attacker.
After back-to-back losses to the Islanders, a team they've dominated in recent years, the Penguins will try to get back on track when they head to Buffalo to face the red-hot Sabres on Friday.
"When things go your way for a while, it’s tough to be losing like that," Fleury said. "Got to learn from it and just try to put it behind us and be ready for tomorrow night."
Staal said it's more important for the Penguins to get back to playing well again, rather than focusing on catching the Rangers.
"We’ve got to worry about our game," he said. "The standings will be the standings. We want to win games. Right now, we’re not playing our best hockey and we’re losing games. That’s definitely something we’ve got to address first."