Oliver Wahlstrom, Jean-Gabriel Pageau and Brock Nelson also scored, and Mathew Barzal had two assists for the Islanders in the opener of a four-game road trip. Semyon Varlamov stopped 36 shots to win for the third time in his last four starts.
''We were well-prepared and I thought the guys battled hard,'' Pageau said. ''A lot of sacrifice, a lot of blocked shots, a lot of battles that we won, and (Varlamov) in net was outstanding. He made some really amazing saves for us.''
Claude Giroux had a goal and an assist, Drake Batherson also scored and Tim Stutzle added two assists for the Senators. Cam Talbot finished with 31 saves as Ottawa fell to 1-7-1 in their last nine games.
''I think we did a lot of good things,'' Giroux said. ''We had a lot of chances, we played well offensively and I thought we were going to come back and tie it up.''
With the score tied 1-1 in the second period, Dobson stepped into a clearing attempt by the Senators along the boards inside the blue line and fired a shot that beat Talbot for his fifth with 6:45 left.
Pageau made it 3-1 with a power-play goal at 8:21 of the third as he backhanded the rebound of Dobson's one-timer from straightaway inside the blue line. It was his second.
Giroux cut the lead to 3-2 off a behind-the-back pass by Brady Tkachuk with 6:52 remaining. It was his eighth.
With Talbot pulled for an extra skater as Ottawa looked for the equalizer, Nelson scored an empty-netter to seal the victory.
''We had two good chances at the end of the game, but there was lots of time left and we have to hold on to the puck and wait until there's a breakdown,'' Giroux said. ''It's something we've worked on, but something we have to keep working on.''
The Islanders took a 1-0 lead on Wahlstrom's power-play goal midway through the first period.
''It's nice to score the first goal, that's for sure,'' Islanders coach Lane Lambert said. ''We've had some comebacks, too, but tonight I thought we did a really good job with the lead and it was really a character win. We fought through a lot of adversity tonight.''
Ottawa managed to tie it during a brief 5-on-3 advantage at 8:48 of the second as Batherson one-timed a pass from Stutzle for his second goal in 11 games. It was the Senators' only goal on six power-play chances.
GIROUX HEATING UP
Giroux is on a nine-game point streak with six goals and seven assists during the stretch. Giroux has more points against the Islanders than any other opponent, with 24 goals and 46 assists in 65 games.
The game had a rare 5:30 p.m. start as the Senators allowed fans to watch former star Daniel Alfredsson's induction into the Hockey Hall of Fame. The early start made for a small crowd, but they showed their respect for Alfredsson, who spent 17 seasons with the Senators, by chanting his name at 11:11 of each period in honor of his No. 11.
The induction was shown on the big screen following the game and numerous players joined fans to watch Alfredsson's acceptance speech, including current captain Tkachuk.
''He's a legend here and it was important for us to show our support to him and almost say thank you for everything he's done for us,'' Tkachuk said. ''It's an amazing accomplishment and achievement that he gets to celebrate with family and friends. It's well deserved.''
Islanders: At Nashville on Thursday night.
Senators: Host Buffalo on Wednesday night.
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