Greiss made 35 saves and Josh Bailey, Brock Nelson and Anders Lee scored second-period goals to the lead the Islanders past the Winnipeg Jets 4-1 Sunday night.
It was the first win of the season for the Islanders, who lost their home opener 2-1 to Washington on Friday.
"It's always good to get the first win out of the way," said the 33-year-old Geiss, who won 23 games last season with a career-best 2.27 goals against average while splitting time with Robin Lehner. "The guys did their part and I did mine."
The Jets lost for the second time in three games in the New York area to start their season. Winnipeg lost 6-4 to the Rangers in their season opener Thursday, and beat the New Jersey Devils 5-4 in a shootout Friday. The Jets are opening the season on a four-game trip that wraps up Tuesday in Pittsburgh.
After a scoreless first period, Bailey put the Islanders on the board, tipping in a power-play goal at 1:51 of the second. Anthony Beauvillier and Devon Toews picked up assists.
It was the third straight game the Jets had allowed the opening goal.
Nelson made it 2-0 at 4:38, sending a shot past goaltender Laurent Brossoit, who started his second straight game and finished with 29 saves. Bailey and defenseman Ryan Pulock assisted on the goal.
Lee stretched the Islanders' lead to 3-0 at 15:55 with his first goal of the season, assisted by Scott Mayfield and Jordan Eberle.
"It was a good rebound game for us," said Lee, the team captain who signed a new seven-year $49 million contract in July. "We were more crisp and Greiss played a great game for us."
The game before a crowd of 9,923 was originally scheduled to be played at Barclays Center in Brooklyn, but was moved to Nassau Coliseum last month. It was the first time in the building's history — which dates to 1972 — the Islanders played a Sunday night home game at the Coliseum. They only twice had played Sunday afternoon games on Long Island.
Patrik Laine put the Jets on the board at 17:06 of the second, snapping a shot past Greiss for his first goal of the season. The Islanders were one of two teams the 21-year-old Laine hadn't scored against. Columbus remains the other.
Blake Wheeler and defenseman Anthony Bitetto, a Long Island native, were credited with assists on Laine's goal.
Beauvillier scored for the Islanders at 1:25 of the third, with assists going to Leo Komarov and Derrick Brassard, his first point as a member of the Islanders.
The Jets outshot the Islanders 15-9 in the opening period. The Islanders dominated the second period with a 19-9 advantage in shots.
"They've got a lot of guys who can shoot. They are a good team," Islanders coach Barry Trotz said of the Jets. "Greiss was really solid."
Brossoit played well despite the loss. His best early save came when he stopped of Komarov on a short-handed breakaway at 13:10 of the first. Brossoit also made two short-handed saves on Nelson in the same sequence midway through the second.
"He was fantastic. When you play as well as he played, you deserve a better number," Jets coach Paul Maurice said. "He's been like that all through camp. He made some great saves and gave us a chance to hang around."
The Islanders started Greiss in goal after newcomer Semyon Varlamov played in the opening loss to Washington on Friday.
Greiss shared the William M. Jennings Trophy with Lehner last season when the Islanders allowed the fewest goals in the league.
"We didn't give them too much room," added Greiss, who stopped all 12 shots he faced in the third period to cement the victory. "We played hard."
NOTES: The Islanders scratched forwards Tom Kuhnhackl and Ross Johnston and rookie defenseman Noah Dobson, who has yet to make his NHL debut. ... The teams meet again Oct. 17 in Winnipeg. ... Winnipeg scratched forwards Bryan Little and David Gustafsson and defenseman Josh Morrissey, who sustained an upper body injury during warmups. ... Islanders coach Barry Trotz passed Hall of Famer Al Arbour on the all-time games-coached list with 1,608, third-most in league history.