"It was nice not being a one-goal game for once," said Turris, who scored his eighth of the season. "We played our game and finished strong."
Zach Bogosian scored the lone goal for the Jets (15-12-2). Ondrej Pavelec made 38 saves, but Winnipeg's three-game winning streak was snapped.
Trailing 2-0 heading into the third, the Jets finally beat Lehner at 3:26 as Bogosian's shot from just inside the blue line made it through traffic and just under the crossbar.
Evander Kane had a great chance to tie the game midway through the period on a 2-on-1 break, but was robbed by Lehner, who made a great pad save.
"We've seen a lot of good things from Robin, but maybe Lehner is Irish," Senators coach Paul MacLean said jokingly. "He was outstanding. The difference in the game was Robin."
Ottawa had a scare when Winnipeg's Dustin Byfuglien knocked Lehner down, and the goalie needed a few moments to gather himself before he got back up.
"I don't remember much," Lehner said. "It was a big body coming at me, and he hit me in the head, but fortunately I felt good after a little while and could finish."
The Senators made it 3-1 with a power-play goal by Turris, and 1:15 after that, Silfverberg scored his second of the game to give Ottawa a three-goal edge.
Ottawa went 2-for-4 on the power play, an impressive feat because the Jets had gone 11 games without giving up a power-play goal.
"They made some nice plays," Jets coach Claude Noel said. "They made a dot-to-dot play that's really tough on your goalie. You've got to give them credit. They can make those plays."
Fatigue seemed to be a factor for the Jets, who played for the third time in four days. Ottawa dominated the first period, jumping out to a 2-0 lead and outshooting Winnipeg 19-6.
"I think the fact we played three games in four days, and not really playing with enough of four lines really caught up with us," Noel said. "I can't fault the players for their effort. I thought they worked hard and tried to come back in the second period. It was a factor, no doubt."
The Senators opened the scoring at 3:44 when Daniel Alfredsson fought his way down the side boards to the front of the net where the puck bounced in off Latendresse.
The Senators made it 2-0 with a power-play goal with 1:21 remaining in the period. Sergei Gonchar made a pass across the crease to Silfverberg, who managed to handle a bouncing puck and beat Pavelec up high.
"It wasn't our best game, that's for sure," Pavelec said. "They came in hard on us, and I think they were a better team."
Gonchar extended his point streak to seven games with assists on goals by Silfverberg and Turris.