"We knew they were a desperate team and we knew it was going to be a tough game," Bailey said of the Senators. "They came at us pretty hard."
Bailey, playing in his 400th NHL game, scored a power-play goal in the first period and assisted on Casey Cizikas' winner midway through the third. Bailey outwaited goalie Craig Anderson and slid the puck into the crease from behind the goal line to Cizikas.
Milan Michalek's power-play tally 6:41 into the third period was the lone goal for the Senators, who had won three straight.
The goal came exactly 110 minutes after the Senators' previous score, not counting one in the shootout of Monday's 2-1 win over the Carolina Hurricanes.
Michalek was at the side of the net when he jammed a loose puck past Nilsson with four players down in the crease.
"I thought I had a glove on it, but it's tough," Nilsson said. "It was so fast, and it was tough for me to know and tough for the ref to see. Those goals happen. They did a good job crashing the net, and the puck came loose, so credit to them.
"We battled hard, and everyone stuck up for each other. Everybody is doing a hell of a job and battling hard, and that's why we keep on winning."
Ottawa had earned at least one point in five straight games.
"We didn't score goals, and you're not going to win hockey games when you don't score goals," defenseman Marc Methot said. "It's deflating, for sure. It's funny because I thought we played pretty good hockey. We just couldn't bury it when we had opportunities.
"We were riding a pretty nice high despite our situation in the standings. When you're stringing together wins at any point in the season it feels good, so we're going to keep rolling and keep trying to get wins."
Bailey had the only goal through the first two periods, beating Anderson with a snap shot from the circle with 2:51 left in the first.
"We played a really solid game five-on-five, and the difference was special teams," said Anderson, who made 25 saves. "That's the way this game is, and some nights, you're going to generate lots of opportunities on the power play and some nights you're not."
The Senators had killed 34 seconds of a 5-on-3 Islanders advantage but couldn't escape the back end of the two penalties.
It wasn't the only special-teams opportunity for New York, but Cal Clutterbuck failed to score on three short-handed scoring chances.
Clutterbuck was stopped by Anderson on a breakaway early in the first. Later in the period, he slid the puck through the crease along the goal line while facing an open net.
Clutterbuck had another short-handed breakaway in the closing seconds of the game, but his shot sailed over the net.