MacKenzie Blackwood, who was making his first start since Feb. 19 because of a lower-body injury, made 25 saves.
"It's my first time we're in playoffs, so it's exciting times," Blackwood said. "It's a great group here. We're excited to see what we can do, and we have a lot of belief in the room."
Tim Stutzle
had two assists, and Dylan Ferguson made 30 saves for the Senators (35-33-5), who fell seven points behind the Pittsburgh Penguins for the second wild card from the Eastern Conference.
"That's a good team, some speedy forwards," Ottawa coach D.J. Smith said. "I thought we had some looks in the third period, and we did everything that we could. We tried. They just find a way to win."
Brady Tkachuk scored on a wrist shot from the left face-off circle to give Ottawa a 1-0 lead at 3:14 of the first period.
"We knew they were on the second end of a back-to-back (New Jersey lost 5-4 to the Buffalo Sabres on Friday), so we knew they were going to be humming there early," Tkachuk said. "It's frustrating because it's crucial at this point in the season, so definitely frustrating."
Hughes tied it 1-1 with a power-play goal at 10:21. He skated end-to-end down the middle of the ice and past three Ottawa defenders before scoring his 40th goal of the season five-hole on Ferguson.