Tyler Seguin and Wyatt Johnston each had a goal and an assist, and Roope Hintz had two assists for the Stars (7-3-1), who won the third game of their current six-game homestand. Jake Oettinger made 17 saves.
Matthew Schaefer, Kyle Palmieri, and Brayden Schenn scored for the Islanders (5-4-2), whose five-game point streak (3-0-2) ended. Bo Horvat had two assists, and Ilya Sorokin made 32 saves.
The Stars win spoiled the return of Islanders coach Peter DeBoer, who coached Dallas for three seasons from 2022-25.
Johnston scored at 4:10 of the third period with a wrist shot from the slot to give Dallas a 4-3 lead.
Robertson scored his second goal on a breakaway at 9:45 to give Dallas its first two-goal lead of the night at 5-3 after getting a stretch pass from Seguin.
Mikko Rantanen scored at 13:02 on a wrist shot after receiving a drop pass from Lian Bichsel for the 6-3 final.
Seguin gave Dallas a 1-0 lead at 11:31 of the first period, finishing off a 2-on-1 with Jamie Benn.
Schaefer scored for the Islanders at 13:43 to tie it 1-1 during 4-on-4 play. The defenseman skated down the left side before snapping the puck just over Oettinger’s right shoulder and under the crossbar.
The 19-year-ol passed Bobby Orr for the second most goals by a teenage defenseman in NHL history. He has 25 goals in 93 games.
Robertson scored during that same 4-on-4 play at 14:32 to make it 2-1 Dallas. He knocked down a pass attempt from Brayden Schenn behind the net and skating in front and wristing a shot past Sorokin’s glove from point-blank range.
Palmieri tied the game back up 2-2 at 4:01 of the second period. Ryan Pulock shot the puck from the point shortly after a faceoff, and the rebound kicked off the end boards and right to Palmieri, who beat a recovering Oettinger with a backhand shot.
Justin Hryckowian made it 3-2 for Dallas on the power play after a Thomas Harley point shot rebounded off the boards above the goal line in the second period. Hryckowian’s backhanded effort found the net at 10:52.
Schenn knotted the game 3-3 after Anthony Duclair fed him a puck from behind the net out above the crease, where he sent a quick snap shot past the blocker of Oettinger at 17:45.