Greiss, who was making his eighth straight start, made 32 saves in a 4-0 win at the Boston Bruins on Monday. He has two shutouts this season and six in his NHL career.
"From top to bottom, it was a great effort led by our captain and our goalie," Weight said.
Kari Lehtonen made 33 saves for the Stars (19-20-8) and was a big reason the Islanders finished 0-for-7 on the power play.
"I think we had some good kills but took too many penalties," Lehtonen said. "We have to stay out of the box. It was nice to get some quality two-minute penalty kills."
Tavares scored the first shorthanded goal of his NHL career with 3:06 left in the third period to give the Islanders a 2-0 lead. De Haan scored with four seconds remaining.
"It only took me 7 1/2 years, so it was nice to get it," Tavares said. "I'm getting more comfortable on the penalty kill and had two good opportunities. It was nice to bury the second one."
Tavares scored from the slot 13:31 into the first period to give the Islanders a 1-0 lead. Greiss made 10 saves in the first; his best was against Tyler Seguin at the left post during a Dallas power play.
"It doesn't take much for a guy like Tavares to get loose and get a breakaway; he had an awesome game and on every shift he was really dangerous," Lehtonen said.
Dallas is 3-12-4 in the game following a victory; the Stars won 7-6 at the New York Rangers on Tuesday. They haven't won back-to-back games since Dec. 27, when they won the second of three straight.