Bill Guerin also scored for New York, which had lost three straight (0-2-1).
Bailey, who made his NHL debut on Tuesday, recorded his first point when he set up Okposo's second goal of the season 12:42 in, a power-play tally that tied it at 1.
"After last game, it's good that Coach [Scott Gordon] shows that confidence in me because, then when I get out there I have confidence, too, because he sent me out there in those situations. I'm just trying to make the most of it," said Bailey, selected ninth overall in this year's draft, held at Scotiabank Place -- the Senators' home arena.
Gordon is impressed with the 19-year-old center's "puck poise."
"Just the patience that he has to protect the puck, put it into areas where he can get a read and get a look and find plays," Gordon said. "That to me is the biggest thing that he's got going for him."
Hunter gave New York a 2-1 lead with an unassisted effort on another man advantage 17:30 into the second. Guerin scored his sixth of the season early in the third.
Filip Kuba netted his first goal on a power play 1:53 in for Ottawa, which lost its third in a row after a 4-0-1 spurt.
"Five-on-five, we were struggling to create some chances and get quality," Senators center Mike Fisher said. "For whatever reason, it's not happening. It's disappointing, for sure, but we've got to just keep plugging away and sticking to the plan."
MacDonald made his sixth straight start for the Islanders. He has started eight of nine games since No. 1 goalie Rick DiPietro was injured.
"Last week, we just had a couple of bad third periods," MacDonald said. "We could have been 3-1 or 4-0, and tonight we came out and played the full 60 minutes and won 3-1."
Ottawa's Alex Auld made 29 saves in his eighth start in nine games.
Islanders defenseman Thomas Pock was given a major penalty and a game misconduct 15:44 into the third period for elbowing Ottawa's Ryan Shannon. Shannon, who made his Senators debut, had to be helped off the ice to the dressing room. He did not return and there was no word on his condition following the game.
"I didn't mean to hit him like that," Pock said. "It is what it is. I've got to give him a call later. I talked to him before the game, you know, I've known Ryan for a long time now -- we played in college against each other. It's always bad and I feel bad about it. It was a bad play, that's all I can say about it. I hope he's all right."
New York's Richard Park was called for slashing with 45.2 seconds remaining but Ottawa, which had pulled Auld, was unable to score with a 6-on-3 skating advantage.
"That made things interesting," MacDonald said.
began serving a two-game NHL suspension for elbowing Montreal's Maxim Lapierre in the head Tuesday in Ottawa's 4-0 road loss. Ruutu will also sit out Saturday against the Islanders on Long Island.
Senators coach Craig Hartsburg wondered how the league will handle Pock's hit on Shannon.
"[Ruutu] got two minutes for what was basically a shoulder," Hartsburg said. "I'm not sure how many games that's going to be worth."
New York held a 16-5 shots advantage in the first, including four before Islanders forward Sean Bergenheim was called for hooking at 1:09.
Ottawa took advantage on the power play when Kuba scored his first goal in 16 games on the Senators' first shot. Kuba, who leads the Senators with 14 assists, one-timed Jason Spezza's pass from the left side, driving a slap shot past MacDonald from the high slot 1:53 in.
Bailey, who debuted Tuesday during the Islanders' 3-1 home loss to Philadelphia, made a fine pass on the tying goal. Okposo received the puck in the slot and fired it into a wide open left side.
Hunter put the Islanders ahead 2-1 when he backhanded a loose puck in the crease past Auld after Kuba was unable to clear it following a faceoff.
"For us, it's pretty simple -- if you skate, you're going to put teams on their heels and our guys did that," Gordon said.
Guerin scored 2:31 into the third, finishing off Doug Weight's pass across the crease from the right edge.
Okposo recovered the puck from one of the on-ice officials following his goal before skating over to the Islanders bench and flipping it to a member of the team's equipment staff to keep for Bailey. "He's a good guy, like that," Bailey said. "He wouldn't let that get away." ... Shannon, recalled from Binghamton of the AHL on Wednesday, played with Spezza and Dany Heatley on the Senators' top line.