Georgiev hadn't started since March 19. He has allowed one goal on 55 shots in two starts against the Islanders this season and is 7-1-0 with two shutouts, a 1.71 goals-against average and .947 save percentage in eight starts against them.
"I liked a lot about his game," Rangers coach David Quinn said. "I thought 'Georgie' was sharp, as he usually is against the Islanders. It's not easy to sit as long as he has and come out and play the way he did. I really liked his game."
The Islanders (26-11-4) are 17-2-2 at home and had a four-game winning streak end. Their other regulation loss at home was March 18, 4-3 to the Philadelphia Flyers.
The Rangers and Islanders will play again here Sunday.
"I don't think anyone would say that's what we expect of ourselves," Islanders forward Josh Bailey said. "We certainly strive for more and we'll look to do that on Sunday."
Rookies Alexis Lafreniere and K'Andre Miller scored, and Artemi Panarin had two assists for the Rangers (19-16-5), who lost to the Pittsburgh Penguins 5-2 at home on Thursday.
Rangers defenseman Adam Fox had his 12-game point streak end (three goals, 19 assists).
The Rangers moved into fifth place in the eight-team MassMutual East Division, five points behind the Boston Bruins for fourth place. The top four teams will qualify for the Stanley Cup Playoffs.
"We played really well, great hockey from the start," Georgiev said. "Felt like a playoff kind of game. It was really fun to take part in that."
Semyon Varlamov made 32 saves, and Andy Greene scored his first goal of the season for the Islanders, who have scored six goals in four games since defeating the Washington Capitals 8-4 on April 1. They're tied for first with the Capitals in the East Division.
"We're just off a little bit and that's fine," Islanders coach Barry Trotz said. "It's part of this long season that you're not always going to be at your best every night. Not the result that we wanted, obviously, but hopefully we regroup and Sunday we go from there."
Lafreniere gave the Rangers a 1-0 lead at 6:05 of the second period, scoring off a rebound from the slot. Linemates Kaapo Kakko and Filip Chytil created the scoring chance and each had an assist on the goal.
"The puck just bounced on my stick, so I just had to put it in," Lafreniere said. "They did really good work and I was in the right spot at the right time and lucky it went in."
Colin Blackwell made it 2-0 with a shot between Ryan Pulock's legs at 10:01. It was Blackwell's third straight game with a goal and his sixth goal in the past seven games. He has played with Panarin and Ryan Strome on the second line the past two games.
"It comes with opportunity and you've got to make the most of it," Blackwell said. "I was waiting for my chance. For me, I'm not doing anything out of the ordinary, just going to the right places and getting rewarded for it. The guys around me are making me a better player."