The Swiss-born defenseman took full advantage of the moment, backhanding the puck past Los Angeles' All-Star goalie at 1:36 of the extra session Saturday to lift New York past the road-weary Kings 2-1.
The 34-year-old Streit, who became the Islanders' captain before the season, helped his club get back to NHL .500 (23-23-8).
"I came off the bench, took a pass and made a little move. So I decided to score," said Streit, of his second overtime goal in his Islanders career. "Maybe I surprised them with my speed. It was a great goal and certainly one I will celebrate."
The Kings, who have a league-low 120 goals this season, fell to 26-19-11. They have scored two goals or fewer in regulation in 40 of their 57 games, yet still hold seventh place in the Western Conference.
"We need more consistency," said Kings coach Darryl Sutter, who replaced Terry Murray behind the bench in December. "That's the only answer for us."
Michael Grabner scored his 15th goal at 6:52 of the first, sliding a loose puck past Quick to open the scoring. It was his first goal in eight games.
Evgeni Nabokov made 34 saves to earn the win. In his past three starts against the Kings -- all wins -- he has stopped 103 of 106 shots.
The Islanders are 7-2-2 in their past 11 games as strong penalty killing, tight defense, and Nabokov's fine play have kept them in most games. With his 306th NHL victory, Nabokov moved past former Islanders star Billy Smith into 22nd place on the league's career list.
"Nabby is playing great," Moulson said. "It was a big win in an intense game. We just have to keep it going."
Islanders coach Jack Capuano says a positive mindset remains vital for the club as it tries to reach the postseason. The Islanders are 11th in the East with 54 points.
"Every game is so important for us right now," Capuano said. "Fortunately, we got these two points."
The Kings have scored just six goals in five games on their trip, and three came in their lone win, against Tampa Bay. Only center Anze Kopitar and right wing Justin Williams have more than 30 points for Los Angeles. Mike Richards, acquired from Philadelphia in a multiplayer trade last summer, has been a disappointment with 14 goals and 13 assists.
Quick and Nabokov made acrobatic saves and had luck on their side in the third period.
Kings left wing Dwight King hit the post on the power play midway through the third, with Jordan Nolan positioned in the crease, but barely missing on the rebound. The 22-year-old son of former Islanders coach Ted Nolan made his NHL debut after he and King were called up from Manchester of the AHL.
Quick made a sprawling save on a point-blank shot by Frans Nielsen at 11:37 of the third. Earlier in the period, Quick, 11-4-5 in his past 20 games, made a series of saves on John Tavares and Moulson in front.
"We have to be better next time," Quick said. "We knew they have a good offense that creates many changes. We expected that. We wanted two points and only got one."
The Kings complete their trip Sunday in Dallas.
The game, the only meeting between the teams this season, marked the Nassau Coliseum return for Kings RW Trent Hunter who played 459 games in more than eight seasons for the Islanders. ... Injured Kings forwards Jarret Stoll (lower body) and Simon Gagne (concussion) remain out indefinitely. ... Moulson played his 218th straight game for the Islanders. It was the fifth time Moulson faced Quick, his brother-in-law.