Henrik Lundqvist made 26 saves for the Rangers (16-14-3).
Trailing 1-0, the Rangers applied heavy pressure midway through the third period but Bishop was unflappable throwing his body in front of a Ryan McDonagh shot and using the shaft of his stick to block another.
When the Senators finally relieved the pressure after about a minute, they went down ice and Latendresse beat Lundqvist with a low shot from the faceoff circle. Greening scored into an empty net with just over two minutes to play.
The Senators had the only goal of the opening two periods in a game that was for the most part void of scoring chances up to that point.
Benoit let loose a point shot that found the back of the net with Anton Stralman in the penalty box for tripping.
Lundqvist was visibly upset with McDonagh immediately following the goal. Not only did Lundqvist not see the shot, but he took an elbow to the head from his defenceman just before the puck went in.
McDonagh was in between Lundqvist and Ottawa forward Chris Neil battling for position in front of the net.
Neil won that battle to help the Senators take a 1-0 lead.
Notes: Darroll Powe and Matt Gilroy were scratches for the Rangers Thursday while Mike Lundin and Peter Regin sat for the Senators. … The Senators swept the three-game season series with the Rangers with a 3-2 shootout win in New York and wins of 3-2 and 1-0 at home. … The Rangers entered Thursday's game with the fewest penalty minutes per game average in the NHL at 9.9. … Centre Brian Boyle played in his 300th NHL game Thursday, and 264th with the Rangers. … The Senators are 3-0-0 against the Rangers. … The Senators own the league's best home record at 13-2-3. … The Senators entered Thursday's game with an NHL best 2.06 goals against per game.