The Islanders outshot the visitors 16-6 in the opening period and had a 20-9 shots advantage in the second. Jets goaltender Ondrej Pavelec made a number of key saves in the first as the Islanders had four power-play chances.
Strome banged in a rebound with a man advantage with 12 seconds left in the first, giving the Brooklyn matinee crowd a chance to launch their standard "Yes! Yes! Yes!" chant. Tavares and Kyle Okposo assisted on Strome’s first of the season.
Brock Nelson made it 2-0 on a wrist shot from the right wing at 6:46 of the second after Tavares slid him the puck from the left side. Defenseman Johnny Boychuk also assisted on Nelson’s first goal of the season.
Tavares increased the margin to 3-0 at 10:45 of the second after Pavelec stopped Marek Zidlicky’s shot from the point and the rebound came to Tavares perched to the goaltender’s left.
"From the drop of the puck, we dominated the game," Islanders coach Jack Capuano said. "We just played Islanders hockey."
Tavares also scored the Islanders’ first goal at Barclays Center in their 3-2 overtime loss last Friday. He has four points in three games. He was denied by Pavelec on a penalty shot with 2:15 left in the third.
Josh Bailey added an empty-net goal with 19 seconds left.
"We came out flat and they came out hungry and ready to play," Jets center Bryan Little said. "It was bit undisciplined and bit us chasing the puck."
Greiss — starting in place of Jaroslav Halak for the second time in three games — wasn’t especially tested. But he was steady when he had to be, only allowing a late second-period goal to Mark Scheifele and power-play goal by Dustin Byfuglien at 11:52 of the third.
"Our goaltender made big saves when he had to," Capuano said. "And his communication with our defense alleviated pressure for us."
The Jets — starting their season with a four-game Eastern road trip — opened with wins over the Boston Bruins and the New Jersey Devils. They were seeking the first 3-0 start in franchise history and will conclude the trip against the Rangers at Madison Square Garden on Tuesday.
Pavelec did make a number of key saves early in the first. His best was a toe stop on Tavares just over seven minutes in as the Islanders captain eluded the Jets defense and was alone in front. Pavelec also denied defenseman Travis Hamonic on a breakaway midway through the second and made 40 saves overall.
"They’re a tough team to play, they have a lot of scorers," Pavelec said. "It was too many penalties. For two periods, I don’t think we played our hockey."
Halak missed the game with an upper-body injury. Capuano said before the game that his starting goaltender was still "day to day."
The Islanders have two more home games this week against Nashville on Thursday and San Jose on Saturday. They are playing 10 of their first 15 games at Barclays Center.
"Certainly it’s nice to get the first win here," Tavares said. "We felt better on the ice today. We want to take advantage of being home. It’s still an adjustment every day but it’s coming around."
Notes: The Islanders are 8-3-1 in 12 games against the Jets since the franchise relocated from Atlanta. … Last season, the Islanders were 40-8-4 when they scored at least three goals (including shootout winners) and 7-20-3 when they didn’t.