The loss put an end to the Jets three-game winning streak.
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, but was robbed by Lehner who made a great pad save.
Minutes later the Senators made it 3-1 with a power-play goal by Turris and 75 seconds later Silfverberg scored his second of the game.
Fatigue seemed to be a factor for the Jets, who were playing their third game in four days. Ottawa dominated the first period jumping out to a 2-0 lead and outshooting Winnipeg 19-6.
The Senators opened the scoring at 3:44 of the first as Daniel Alfredsson battled 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 less than two minutes 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.
Gonchar extended his point streak to seven games with assists on Silfverberg's and Turris's goals.
Notes: The Senators LW Kaspars Daugavins was a healthy scratch. Ottawa is without G Craig Anderson (ankle sprain, indefinite), D Mike Lundin (concussion, indefinitely), D Dave Dziurzynski (concussion, indefinite), D Erik Karlsson (Achiles, out for season), C Jason Spezza (upper body injury, indefinite), LW Milan Michalek (knee, indefinite), D Jared Cowen (hip, out for season). The Jets' D Paul Postma, C Alexander Burmistrov and G Al Montoya were a healthy scratch. Winnipeg is without D Tobias Enstrom (shoulder, indefinite), D Zach Redmond (leg, indefinite), RW Anthony Peluso (hand, indefinite), C Jim Slater (upper body, indefinite).