The game briefly got heated at 7:09 of the third period, when Brady Tkachuk skated into Shesterkin, starting a scrum that eventually led to the Rangers' goalie leaving the crease to go after Tkachuk behind the net.
The Rangers ended up on the power play, which became a 5-on-3 when Michael Amadio took down Shesterkin behind the net and was whistled for goalie interference at 8:37.
Artemi Panarin scored on the 5-on-3 to make it 4-0 at 9:01. It was his 20th of the season.
Will Cuylle extended the lead to 5-0 with a power-play goal at 9:57.
"There's not much that went our way," Senators defenseman Thomas Chabot said. "We created some stuff, but at the end of the day it's just not the hockey that we've been playing lately. You can be frustrated with the loss and everything, but at the end of the day you've got to be realistic. We've been playing some really good hockey, a lot of it on the road. You know what, you've just got to look forward to the next game at this point."
NOTES: The Senators have scored two or fewer goals in 11 of their past 14 games. … Shesterkin has back-to-back shutouts for the fifth time in his career, making him one of three goalies in Rangers history to have as many as five sets of back-to-back shutouts, joining Lorne Chabot (six) and Ed Giacomin (five).