Clutterbuck made it 2-0 at 13:05 with a shot from between the circles after Casey Cizikas won a puck battle behind the net.
Giroux cut it to 2-1 on a 4-on-3 power play at 6:52 of the second period with a long wrist shot that found its way through traffic.
Chychrun tied it 2-2 at 12:25 when his wrist shot beat a screened Sorokin.
“We tried making that effort about him, and we tried to win that game for him,” Senators captain Brady Tkachuk said of Brannstrom. “Just what he means to our locker room, it’s emotional. You never want to see that, especially as good of a guy as he is.”
Sorokin stopped all 16 shots he faced in the third.
“We definitely want to be better in front of him [Sorokin],” Horvat said. “That’s staying out of the box and playing 5-on-5. And when you give up those penalty kills, it's going to be tough on your goaltender, but he was a brick wall in there again tonight.”
NOTES: Dobson extended his point streak to five games (one goal, five assists) and played 27:42. … Barzal extended his point streak to five games (one goal, four assists). ... Senators defenseman Travis Hamonic played his 800th NHL game. He was a second-round draft pick (No. 53) by the Islanders in 2008 and played his first seven seasons for them. … Giroux has 73 points (26 goals, 47 assists) in 68 games against the Islanders; only Pittsburgh Penguins centers Sidney Crosby (132 points; 41 goals, 91 assists in 88 games) and Evgeni Malkin (85 points; 32 goals, 53 assists in 74 games) have more against them among active players. … Chychrun had a game-high nine shots on goal in 28:12.