Marty Turco rebounded from a bad night by stopping 24 shots.
Turco was pulled in the second period Wednesday against the Devils after allowing three goals on 17 shots.
Bill Guerin, Mark Streit and Jon Sim scored for the Islanders, who have allowed 12 goals in their last two home games.
Rick DiPietro, who served as the Islanders' backup for the team's first four games, started his second straight and first at home. He finished with 24 shots. New York is 3-1-1 against Dallas at home in the last five meetings.
Dallas took an early lead on its first power-play opportunity when Eriksson tipped in a pass from the right point by Ribeiro at 3:30. The Stars have scored first only twice in eight games this season and have been outscored 32-23 overall.
Ribeiro earned the key assist again when Morrow tapped in a shot during a rush to make it 2-0 at 14:13.
The Stars pushed their lead to three with 98 seconds left in the period, just as their second power play expired. Eriksson scored from in-close, and Ribeiro set up the goal with another primary assist.
The Islanders had many scoring chances in the second period, including a two-man advantage for a full two minutes, but they were blanked.
They finally broke through at 10:16 when Guerin banged home a rebound to get New York within 3-1.
Dallas went back up by three at 13:05 when Barch found the puck on his stick and ripped a shot past DiPietro off another assist by Ribeiro.
Ribeiro finally scored one of his own when he fired a pass from Mike Modano by DiPietro during a power play with 93 seconds left in the second period.
Streit connected for his first goal of the season, a power-play tally, at 3:28 of the third period. Sim scored the final goal with 2.1 seconds remaining in the game.
Notes: Islanders D Brendan Witt didn't return after a knee-to-knee collision with Barch in the first period. The team said it was an undisclosed lower-body injury, and that Witt would be re-evaluated Friday. ... The only Stars with plus ratings entering the game were Modano, Joel Lundqvist and B.J. Crombeen - all at plus-1. Despite a promotion of buy one ticket, get one free, Nassau Coliseum was less than half-full at the start of the game. The announced attendance was 10,183.
