Anders Lee had a goal and an assist, and Mikhail Grabovski also scored to help the Islanders win for the fourth time in six games and improve to 4-0-1 in their last five against the Stars. New York was coming off a 5-2 loss at Pittsburgh on Saturday night.
“We’re feeling good,” Okposo said. “It was key for us to come back strong after last night in Pittsburgh. They are a heck of a team over there.”
Thomas Greiss finished with 36 saves for the Islanders.
New York trailed 2-1 in the first period before scoring the next four goals and then held off Dallas in the third to improve to 12-4-1 against Western Conference teams.
The Stars, coming off an overtime defeat at New Jersey the previous night, lost consecutive games for the first time this season. Dallas was the last remaining NHL team without back-to-back defeats.
The Islanders, 1 for 14 on the power play over their last six games, went 2 for 6 against the Stars.
Clutterbuck, who left Saturday night's game at Pittsburgh with an upper-body injury, was briefly knocked out of this one at 5:07 of the second after a high hit by Dallas' Jason Demers.
"I feel good and we're feeling good," Clutterbuck said. "The key is to keep this going and peak at the right time."
Demers was issued a major and a game misconduct, ending his night.
"I think the guy that got hit has a history of diving," Stars coach Lindy Ruff said. "I looked at the play, I don't think he elbowed him. I don't think he did anything, really. And (Clutterbuck) didn't seem to be hurt. But he sold a pretty good one. Maybe (Demers) deserved a minor penalty."
During the ensuing 5-minute power play, Okposo didn't get a clean attempt on a rebound of Nick Leddy's shot. The puck was headed wide left of the net but caromed off defenceman Alex Goligoski's skate and trickled in near the right post at 8:13.
With just under 5 minutes to go in the period, Grabovski took a pass from Ryan Strome at the right side of the net and fired it past Lehtonen to make it 4-2.
Clutterbuck extended the Islanders' lead to three with 2:17 left in the period.
Nichushkin pulled the Stars to 5-3 at 1:46 of the third when his shot deflected in off Leddy's skate.
Clutterbuck restored New York's three-goal lead near the midpoint of the period.
Nichushkin got Dallas back within two on a power play less than 30 seconds later, and Spezza pulled the Stars to 6-5 with 1:42 left.
"That's a good hockey team," Islanders coach Jack Capuano said. "Our power play did a great job. We created momentum. This was a good win for us."
The Stars, tops in the league with 60 points, have lost four of six (2-2-2).
"We haven't played our best, obviously," Goligoski said. "We're mentally not there. We have to reset and reset quick. We have a bunch of games coming up."
Fiddler put the Stars on the scoreboard first, knocking in a rebound of a shot by Radek Faksa at 5:55 of the opening period.
With Dallas on the power play, Jamie Benn was whistled for a double-minor for high-sticking midway through the first. Less than 20 seconds later, Cody Eakin was also called for high-sticking, putting the Islanders on a 4-on-3 advantage.
The Islanders quickly tied it as Okposo found Lee below the left faceoff circle, and Lee skated in and fired a shot past Lehtonen with 9:26 left in the opening period.
"When we spend the amount of time we did killing penalties, there's a lot of bad stuff that's going to happen," Ruff said.
The Stars took a 2-1 lead when Sharp tipped in a shot by Goligoski with 6 1/2 minutes left in the first. It was Sharp's 16th of the season.
Okposo's first goal of the game tied it again late in the period. Thomas Hickey fired a shot from the right slot, and the rebound came to Okposo, who whacked the puck as he was falling forward with 1:32 to go.
NOTES: The Stars continue their stretch of three games in four days against the New York-area teams when they face the Rangers at Madison Square Garden on Tuesday night. ... Dallas fell to 15-6-1 against the Eastern Conference, including 8-2-1 vs. the Metropolitan Division. ... After holding opponents scoreless on the power play in a franchise-record 15 consecutive games (totalling 35 chances), the Islanders have allowed man-advantage goals in three straight games. ... New York D Johnny Boychuk missed his second straight game after being placed on injured reserve Friday. ... The Islanders began a stretch with eight of 10 games at home.