Tim Stutzle scored the lone goal for the Senators, who were playing the second half of a back-to-back and coming off a 3-2 overtime loss to Boston. Filip Gustavsson made 31 saves in his first NHL start since Dec. 7.
The Rangers outshot the Senators 15-7 in the second and took a 2-1 lead as Panarin scored a power-play goal midway through the period.
''He's a great player, he's a star player for us,'' Rangers coach Gerard Gallant said. ''He makes those great passes and tonight he shoots the puck and buries the winning goal on the power play. He's a big part of our group and, obviously, when the power play is going like they're going, and to win another hockey game for us tonight, that's huge.''
Senators coach D.J. Smith thought there was a clear advantage in the game for the Rangers.
''The power play is the difference tonight for them, Panarin is one of the best players in the league,'' Smith said. ''He's the difference at the end of the day.''
A balanced first period saw the two teams exchange goals with Stutzle opening the scoring at the four-minute mark when he took advantage of a Rangers turnover and wristed a shot past Shesterkin.
Just over three minutes later, Braden Schneider fired a shot from the point that didn't get through - but Strome was able to pick it up and beat Gustavsson for his 10th of the season to tie it.
Trailing 2-1 to start the third, the Senators looked for the equalizer and had a good chance with a power play midway through the period, but were unable to beat Shesterkin.
''I don't know if he's the best goalie in the league, but he's close,'' Smith said of Shesterkin. ''You can see it on his play and whatever his record is.''
With just over a minute left in regulation, Shesterkin nearly sealed the game with an empty-net goal, but the puck went just wide.
''The sound (from the bench) was getting louder and louder as the puck got closer to the crease,'' Strome said. ''It's just a matter of time - he's going to stick with it. ... It's not just trying to score goals; the plays he makes and the breakout passes are just spectacular. He's probably a better passer than 75-80% of our team. I think guys would openly admit that, too.''
NOTES: New York improved to 14-2-1 against Atlantic Division opponents and 20-5-1 against teams in the Eastern Conference. ... Panarin had his 17th multi-point game of the season and seventh in his past 12 games.
Rangers: Host Washington on Thursday night.
Senators: Host Minnesota on Tuesday night.
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