Tkachuk, who was playing in his 500th NHL game, cut it to 2-1 at 4:06 of the second when he tipped a Nick Jensen point shot.
"It's been an emotional 24 hours for not only him but the rest of our group (after trading forward Josh Norris and defenseman Jacob Bernard-Docker on Friday)," Green said. "And having a 12:30 p.m. start, I give our team a lot of credit for getting focused to play [today]. The guy's the captain of our team. He's maturing a lot as he goes along, as well."
Panarin extended his goal streak to four games when he took a stretch pass from Jonny Brodzinski, skated in on a breakaway and beat Ullmark over the glove with a snap shot to make it 3-1 at 7:08 of the third.
Cozens, who was acquired by Ottawa with Dennis Gilbert in the trade on Friday, had an assist on Greig's goal.
"It felt great," Cozens said. "You couldn't draw it up any better. A little comeback win in overtime for the first one. It was an awesome win. I'm so, so happy and excited to be a part of
this group and do something special here."
NOTES: Stutzle's point streak is the third longest in franchise history behind Dany Heatley (22 games in 2005-06, 16 games in 2006-07). … Cozens had a career-high nine hits in 17:27 of ice time. Gilbert had three hits in 6:19 of ice time in his Ottawa debut. … Tkachuk became the first player in Senators history with multiple goals in his 500th NHL game. … Panarin's 150th multi-point game with New York tied Steve Vickers for seventh most in team history. … Senators defenseman Travis Hamonic needed help getting off the ice late in the third period and did not return. Green did not have an update.