Jason Spezza's assist on Hintz's goal was his 900th NHL point (328 goals, 572 assists) in his 1,009th game. Ben Bishop made 37 saves.
The six goals were the most Dallas (11-7-2) has scored in a game this season. The Stars are 3-1-1 in their past five games. They play the New York Rangers at Madison Square Garden on Monday.
"With back to backs, it was really important that we could really spread the [ice] time in the third period, which is a luxury in this League," Montgomery said. "If our big line doesn't have the night they had, it's still 3-1, 3-2 there right down to the end."
The Islanders (10-7-2) lost in regulation at home for the first time since Oct. 6, ending a seven-game home point streak (5-0-2).
Thomas Greiss made 16 saves before he was replaced by Robin Lehner (11 saves) in the second period. Anthony Beauvillier and Scott Mayfield each scored.
"I thought our battle level came down and you can't; you know they're going to raise their battle level," Islanders coach Barry Trotz said. "I thought a couple guys tried to go around the game instead of through the game, and you can't do this in this league. And I thought some guys got pushed out of the game and that's not good enough. We were really easy to play against tonight. We weren't hard, and that's not us."
Beauvillier, who had a hat trick against the Rangers on Thursday, gave the Islanders a 1-0 lead at 3:36 of the first period.
But the Stars scored four straight goals in the second, starting with Lindell's first at 2:09, when he beat Greiss with a wrist shot through traffic to make it 1-1.