Ponikarovsky broke the deadlock 5:57 into the third period. The Senators had no answer against Montoya, who made 33 saves in place of ailing Ondrej Pavelec (flu) and posted his first shutout of the season and third of his NHL career.
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"The team really battled for me," Montoya said. "I felt for the start of every period we were in control of the puck, and sometimes you want to see shots, but I felt good and I felt comfortable out there.
"I felt like I did everything to prepare for this game."
Like Montoya, Bishop made just his second start of the season as Craig Anderson got the day off. Bishop finished with 36 saves.
"Ben Bishop was outstanding," Ottawa coach Paul MacLean said. "He really played well, but we weren't even good enough.
"The last 10 minutes after they scored is when we actually started to play. They were way better than us. Montoya played very well for them. We had 80 attempts at the net but we didn't have enough people at the net."
The Jets did just enough to win.
Kyle Wellwood intercepted a clearing attempt and took a shot from inside the blue line that Ponikarovsky deflected in off Bishop's shoulder and both posts.
"It was a pretty good game, and everyone battled for every inch of the ice. Overall, the guys did a good job," Ponikarovsky said. "We had a couple opportunities to score, but it didn't go in.
"We just stuck with the game plan, and it happened to be me who got the goal, but everyone worked hard. I'm just glad to get the goal for the team."
The Jets (5-5-1) won for the second time in six games and snapped a three-game road skid.
The Senators (6-4-2) have scored just seven goals in past five games, including four in a 4-3 win over the Buffalo Sabres on Tuesday.
The Senators have lost a pair of 1-0 decisions in that span. Ottawa has allowed only 15 goals in eight games.
"Collectively, we have to come together and find a way to create offense, put pucks and bodies at the net, and gain more offensive zone time. I have to do a better job of that myself," he said. "We know we can do a lot better, we just have to do it more consistently."
Goaltending hasn't been a problem for the Senators, who couldn't produce any offense to get Bishop a win.
"When he's playing that well and giving us a chance, we want to help him out, too, and put at least one or two on the board," Turris said. "Andy and Bish are unreal. They're playing amazing and keeping us in games and giving us a chance to win.
"They do a great job for 60 minutes, giving us a chance, so we have to do a better job helping them out."
The Senators lost Peter Regin to an upper-body injury early in the game after he blocked Grant Clitsome's shot. He will be reassessed on Sunday, but MacLean said the injury isn't related to a shoulder problem that has plagued Regin the past two seasons.
- The Jets entered with the most points from defensemen this season with 34. St. Louis began the day in second place with 31, four more than Ottawa.
- Senators forwards Eric Condra and Colin Greening have both gone five games without a point.
- Jim O'Brien and Andres Benoit were scratched by the Senators. Anthony Peluso and Dustin Byfuglien sat out for the Jets.