"Things weren't going well earlier, and there was some frustration," Morrow said. "It felt good getting back together."
Krystofer Barch also scored for the Stars, who went 2-1 against the three New York-area teams this week. Dallas beat the Rangers 2-1 on Monday and lost 5-0 at New Jersey on Wednesday.
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.
"One of the big differences between last night and tonight was Marty made some big saves early," Morrow said. "It gave us a bit of confidence."
Bill Guerin, Mark Streit and Jon Sim scored for the Islanders, who have allowed 12 goals in their last two home games.
Guerin also praised Dallas' hot line.
"They've got good chemistry," Guerin said. "They had a big night."
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 saves. 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 were also given another power play during that advantage, but again went scoreless.
"Our defense did a great job on the penalty killing, especially that five-on-three," Ribeiro said.
"That was a crucial time in the game, and the special teams came up bit," Morrow added.
Guerin lamented his team's tendency to take penalties.
"We're in the penalty box too much," Guerin said. "Our penalty kill wasn't as sharp as it needed to be."
The Islanders finally broke through at 10:16 when Guerin banged in 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. "It's always a tough situation when a D-man goes down," Islanders defenseman Freddy Meyer said. ... 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.