Roy, who went 130-92-24 in three seasons coaching Colorado from 2013 to ’16, was hired Saturday to replace Lane Lambert after the Islanders went 0-3-1 on a four-game trip.
“I was very nervous, I won’t lie,” Roy said. “You always want to win that first game, and I am very thankful to the players for the effort they put out there. I was just hoping to give a good show to our fans as well.”
In the extra period, Mathew Barzal found Horvat behind the Stars’ defense and Horvat converted a forehand-backhand maneuver to give the Islanders their third win in 11 games (3-6-2).
“It meant a lot. To get a win here on home ice, in Patrick’s first game, it definitely feels great,” Horvat said in his postgame, rinkside interview.
New York tied the score 2-2 when Fasching redirected Dobson’s shot at 5:23 of the third period. Dobson notched his career-high 41st assist on the play.
Romanov opened the scoring at 2:52 of the first period with his fifth of the season.
“We needed two points tonight,” New York captain Anders Lee said. “It’s a great first night to build off of. … [Roy] was into it. He sees the game really well, understands the little things that are working, that aren’t working on the fly and making little adjustments.”
Robertson tied it 1-1 with his 15th goal of the season and team-leading 48th point. The Islanders’ defense lost track of Robertson as he got the puck in the high slot and roofed a forehand shot over Sorokin’s blocker with 8:25 left in the second.
Lundkvist gave the Stars a 2-1 lead with 4:52 remaining in the middle period. Pavelski screened Sorokin, and Lundkvist’s slap shot from the point sailed into the back of the net.
Stars forward Craig Smith left the game with an upper-body injury and did not return.
The Islanders, hoping to stay in the mix in a crowded Eastern Conference playoff race, will take on the Vegas Golden Knights on Tuesday.
“We’re doing it for each other in there, and that’s his main message,” Horvat said of Roy. “And winning some games, that definitely helps.”
The Associated Press contributed to this report.