Shortly after the Islanders took a 2-0 lead in the second period, Capitals coach Bruce Boudreau used his timeout and changed the Capitals' fortunes.
"The timeout was the turning point of the game," Washington center Marcus Johansson said.
Washington is 10-0-3 in its past 13 meetings with the Islanders, including six straight wins on Long Island.
"We played well in the first period, and about 10 minutes of the second period," Islanders forward Kyle Okposo said. "After that, we stopped playing our game, and gave them a couple of chances and they capitalized."
Okposo and Travis Hamonic scored and Montoya made 19 saves for the Islanders, who lost their third straight despite leading 2-0. New York took the first 11 shots of the game without scoring, but grabbed a 1-0 lead with its next shot.
Okposo skated in on a 2-on-1 break, moved from the wing to the slot, and fired a wrist shot that beat Neuvirth high at 13:48.
The Islanders jumped ahead 2-0 just 33 seconds into the middle period when Hamonic took a slap shot from the right point that eluded traffic and Neuvirth, who wasn't impressed by either of New York's tallies.
"I think they got two lucky goals," he said.
Laich cut the Capitals' deficit in half at 9:44 when he sent a wrist shot from the left side between Montoya's pads.
Knuble tied it at 2:24 of the third period when he backhanded a rebound past Montoya. The Capitals can now savor this comeback until Tuesday when those host the Islanders.
"I'm just glad we have a couple of days off, especially with a win," Boudreau said.
Among Washington's scratches were Marco Sturm, claimed Saturday off waivers from the Los Angeles Kings, and goalie Seymon Varlamov. Todd Ford served as Neuvirth's backup. ... The Islanders placed C Rob Schremp and G Nathan Lawson on waivers. ... The attendance was 16,250, the Islanders' biggest home crowd of the season.