Nylander scored with 3:32 left in the third period, and Varlamov stopped 32 shots in his debut to help Washington beat the Montreal Canadiens 2-1 on Saturday night.
Robbed by Jaroslav Halak's spectacular glove save in the second, Nylander finally found the back of the net when he banked a shot off the goalie's pad from behind the goal line.
"I just tried to get it on the net because he was off his post a bit," said Nylander, who hadn't scored since tallying his second of the season in a 4-3 win in Pittsburgh on Oct. 16.
Nicklas Backstrom gave Washington a 1-0 lead with his 10th goal on a power play midway through the first. Backstrom left during the third period after the Capitals had already lost Sergei Fedorov and
Tyler Sloan to injury earlier in the game.
"We only dropped two or three guys, so we were OK, it was an easy night," joked Capitals coach Bruce Boudreau, who has had to juggle his lineups throughout the season and had no updates on the team's latest injuries. "I haven't heard. I'm afraid to go into that room any time."
Patrice Brisebois tied it in the second with his second goal in two games for Montreal, which lost its second in a row to finish 4-2-1 on its franchise-record seven-game homestand.
"Our power play is non-existent because we get outworked by the opposition," Canadiens coach Guy Carbonneau said. "We have an advantage and we don't take advantage of that. That's the bottom line."
Varlamov, who joined the team Friday night during a 5-1 home win over Ottawa, got a bit of help in his first appearance when Montreal's Alex Tanguay hit the post twice. Alexei Kovalev also struck iron moments before Nylander's goal.
"As soon as they missed all those chances I said, 'You know what, it's in the books, right now. It's meant to be that we're going to get lucky and we're going to score one.' And it happened, I think, on the next shift," Boudreau said.
Recalled from Hershey of the AHL on Friday, Varlamov joined the Capitals midway through the first period Friday, taking over from emergency goalie Brett Leonhardt on the bench as Brent Johnson's backup.
"He won the game for us tonight," said Ovechkin, who got his 40th point with an assist on Backstrom's goal.
Jaroslav Halak made 24 saves in his third straight start for Montreal, including a stop 12:42 into the second where he practically snatched the puck off Nylander's stick with his glove.
Kovalev wore the captain's "C" for Montreal, which was without Saku Koivu, sidelined by a lower-body injury he suffered Thursday night in a 3-1 loss to Tampa Bay.
Mathieu Dandenault and Christopher Higgins were lost to injury in Tuesday's 4-1 win over Calgary. Dandenault is sidelined indefinitely after having surgery on Wednesday on his broken left arm, while Higgins is out due to an unspecified upper-body injury.
Backstrom put a rebound of Ovechkin's point shot past Halak 10:19 in, only 9 seconds after Montreal defenseman Josh Gorges was penalized for roughing.
Brisebois drew Montreal even 15:25 into the second. Brisebois took Tanguay's pass during a 4-on-4 situation and drove a slap shot past Varlamov from the top of the right faceoff circle for his third goal of the season.
Leonhardt, the Capitals' Web site producer, signed an amateur tryout contract and dressed for Friday's game after backup Jose Theodore -- who recorded Washington's only shutout of the season in a 3-0 win over his former team on Nov. 28 in the Canadiens' last road game before the homestand -- injured a hip flexor during the morning skate. ... Canadiens C Ben Maxwell made his NHL debut. Maxwell, who was called up along with G Marc Denis from Hamilton of the AHL on Friday, moved into Koivu's spot on a line with RW Matt D'Agostini and LW Andrei Kostitsyn. Denis dressed in place of Carey Price, who is out with a cold. ... Kovalev is in the midst of a 19-game goal drought, tying the worst streak of his career.