Ellis stopped 27 shots.
"Dan made probably three or four great saves to keep the score where it was at," Stars coach Lindy Ruff said. "He made the saves that could have allowed us to win the game, even get a point out of the game."
The Stars' first goal was at 11:45 of the first period. Vernon Fiddler hustled in to pick up the puck against the back boards, and pushed it across to Alex Chiasson. He passed to Whitney skating into the left circle, and his shot went in past Poulin's left leg.
Gonchar then intercepted a pass inside the blue line, skated to the top of the right circle and fired a shot inside the left post at 18:12. It was the first goal of Gonchar's 19th NHL season.
The Islanders began their comeback in the second period. They nearly scored 9 minutes in, but Ellis stopped Colin McDonald's tip from in front of the net.
Okposo then broke through for New York at 10:47 of the second, scoring from low in the right circle. Assists went to Vanek and Tavares.
NOTES: In last Monday's game, Tavares tied a career high with five points. Vanek added two assists, but Okposo missed the game because of the birth of his first child. The line totaled three goals and three assists Sunday. ... Vanek has at least one point in 11 of his last 12 games, with a total of 17 points. ... New York defenseman Travis Hamonic did not play in the third period because he was sick. ... The Stars' six consecutive losses all have been against Eastern Conference teams.