Turris gave the Senators a 1-0 lead with a power-play goal 2:47 in on Ottawa's first shot of the game. Turris was off balance as he deflected Erik Karlsson's point shot past Cory Schneider for his first goal in 11 games.
He added an empty-net goal in the final second of the game.
The Devils, lethargic at the start, picked up their game after falling behind. New Jersey outshot Ottawa 10-4 in the first period but couldn't beat Anderson.
Patrik Elias, activated from the injured list earlier Wednesday, came closest with a drive that rang off the post.
The frustration built for the Devils in the scoreless second period as they outshot the Senators 16-4.
Anderson came up with save after save and stopped Jaromir Jagr twice early in the period. The first was Jagr's power-play blast from the left circle. Anderson later stretched to make a skate stop on Jagr, denying a 2-on-1 break with Scott Gomez.
Anderson was on his toes throughout the period. One of his best stops was made with two minutes left when he turned aside a wrist shot by Elias.
New Jersey kept pressing in the third, and Anderson made early close-in stops on Elias and Adam Henrique.
"We were all over him, getting pressure, but we've got to find a way to get one in," Henrique said. "That game was there for us. It's a tough one to give up."
Anderson almost scored in the final seconds into the empty Devils net, but his clearing shot rolled just wide.
"I've waited my whole life for a chance like that and I may never get it again," Anderson said. "I hooked it a little, considering I'm a lefty. I knew I had to get it up in the air to have a shot. I thought it was in."
The Senators, while happy with the victory, know they won't win many games being outshot 34-16.
"I don't think this was a game that we necessarily deserved to win, but we'll take it," Turris said.
NOTES: The Devils opened a four-game homestand following a stretch of 15 of 20 games on the road. ... The Senators concluded a three-game road trip. They will host Anaheim on Friday. ... The Devils scratched LW Dainius Zubrus (leg laceration), LW Mike Cammalleri (lower body) and D Damon Severson (lower body). Ottawa scratched LW Colin Greening and D Patrick Wiercioch. ... Defenseman Eric Gelinas led the Devils with six shots. Elias had five.