Trailing 5-2 to start the third period, the Rangers had a great chance to get back in the game with a two-man advantage for 85 seconds but failed to capitalize.
The Rangers, who came into the game with points in 17 of their last 19 (16-2-1), had chances throughout the night, but Forsberg was solid when called upon.
Trailing 2-0 after the first, the Rangers looked to get back in the game and while they had a better second period in the end the Senators led 5-2 after 40 minutes.
Panarin had a power-play goal just 39 seconds into the second to make it 2-1, but Tarasenko regained the two-goal lead with his first in 13 games. Miller got the Rangers right back in it scoring 22 seconds later.
Tkachuk scored his second late in the period taking a rebound off the back boards and beat Shesterkin short side.
Despite being largely outplayed at times the Senators came out of the first period leading 2-0.
Tkachuk opened the scoring tipping an Artem Zub shot, and with just under two minutes remaining Giroux beat Shesterkin with a wraparound goal.
Ridly Greig returned to the Senators lineup after missing 10 games with a high ankle sprain.
Senators: Host the Toronto Maple Leafs Thursday night.
Rangers: Head to Washington Saturday to take on the Capitals.
This report by The Canadian Press was first published Dec. 5, 2023.
Lisa Wallace, The Canadian Press