"I didn't have a positive feeling," said Tavares. "I saw it pretty good all the way."
The Senators extended their lead to 4-2 just seconds later. Mark Stone's shot went wide off the boards and Derick Brassard gathered up the rebound and reached back to tuck it past Islanders goalie J-F Berube.
Ottawa eventually added two empty-net goals in the final four minutes.
"Tonight was a good game," said coach Jack Capuano. "It came down to the rebound goal that they got, and that changed the game. We're down 2-0, we're resilient, we come right back. There's a lot of fight in that room."
Anthony Beauvillier tied the game at 2 at 14:07 of the second, but within 30 seconds Thomas Hickey drew a penalty for hooking. Ottawa quickly took advantage on the power play.
Stone set up position in front of the net and punched in a rebound of Erik Karlsson's shot after a Berube deflection. The goal put the Senators up 3-2 at 15:03 of the second period.
"The third goal was a big goal for them, the power play goal that they got," said Capuano. "We had three guys versus their two at the net. That's when you want to talk about lifting a stick, having some battle level in you, having a fight. That to me, that was a big goal for them. They didn't generate much tonight I can tell you that."
With the Islanders trailing 2-0, Anders Lee got the Islanders on the board 27 seconds into the second period with his ninth goal in the last 13 games. After a face-off in the Islanders' zone, Josh Bailey stepped into swipe a clearing attempt from Phaneuf and quickly fed Lee for the goal.
Beauvillier's third career NHL goal got the Islanders even at 14:07 of the second. The rookie broke out as Travis Hamonic recovered a rebound in front of Berube. Hamonic's long pass caught up to Beauvillier cleanly and he beat Ottawa goalie Mike Condon to the stick side to knot the game at 2.
The Islanders next play the Bruins on Tuesday in Boston. Puck drop is at 7 p.m.