Ottawa has lost 18 of 20 games
Grabner, the Islanders' star rookie, scored a short-handed goal for New York and set up Josh Bailey's third-period score.
"Every shift he's out there, you notice him," Islanders goalie Nathan Lawson said. "He's flying around and he always seems to get pucks in great areas. ... It's unbelievable."
Grabner scored eight goals in four games last week, including a hat trick in the Islanders' win at Buffalo on Sunday
Blake Comeau had the other goal in regulation for the Islanders, who have won four straight.
"That's another big step for us because we did not have our best game and we found a way to get two points," right-winger Kyle Okposo said.
The Senators are winless in all nine games they've played this season that have gone to overtime or a shootout.
"It would be nice if we could win a shootout once in a while," Spezza said
After the loss, the Senators traded center Chris Kelly to Boston. The Bruins sent Ottawa their second-round pick in this year's draft in exchange for the 30-year-old Kelly, who had 12 goals and 11 assists this season for the Senators.
On Tuesday night, Brian Elliott finished with 24 saves for Ottawa, which hasn't won at home since Dec. 26.
Ottawa opened the scoring late in the first when Butler snapped a rebound past Lawson during a Senators' power play with just over two minutes remaining in the period.
The Islanders tied it near the midway point of the second.
Jarkko Ruutu's shot from a sharp angle was wild and struck teammate Chris Neil. As Neil fell to the ice behind the Islanders goal and tried to get up and make his way to the Senators' bench, play continued up the other end and Comeau beat Elliott on a rebound. Despite protests from Spezza and Ottawa coach Cory Clouston, the goal stood.
The puck appeared to strike Neil in the chest, but he was OK and was back out later in the period.
Shannon restored the Senators' lead less than five minutes later, beating Lawson with a shot from the point on the power play.
Grabner, who won the fastest skater competition during the skills challenge at the All-Star Game, broke in alone on Elliott with the Islanders shorthanded early in the third.
Despite losing control of the puck and failing to get a shot off, he was quick enough to go into the corner and retrieve it before skating around Ottawa's net and tucking the puck home after Elliott had overcommitted on the initial deke.
After Neil had a goal waved off when he tipped a point shot in with a high stick, Grabner set up Bailey to give the Islanders the lead at 6:39 of the third.
Then with just over four minutes remaining in regulation, Condra fed Karlsson in the high slot and he wired a shot into the top corner to tie the game at 3.
- Spezza got an assist on Butler's first-period goal to record his 500th career point in his 501st NHL game.
- Islanders D Andrew MacDonald took an accidental high stick from Ottawa's Chris Kelly during a first-period collision and had to leave the game for repairs. He returned wearing a full facemask.
- Before the game, the Senators recalled right-winger Erik Condra from Binghamton of the AHL and the 24-year-old made his NHL debut, earning his first point on Karlsson's tying goal late in regulation.