Green, Nylander and Laich each scored during a four-goal first period for Washington, which beat Ottawa for the second time in four days. The Capitals topped the Senators 8-6 on Saturday.
"I think, with the win tonight, we're really starting to believe that we're a good hockey team," said goalie Olaf Kolzig, whose 289th victory moved him into 25th place on the NHL list. "But again, we dug ourselves such a big hole at the beginning of the season; we're just slowly but surely creeping our way back into things."
The Capitals stumbled to a 6-14-1 record at the start before Bruce Boudreau took over for coach Glen Hanlon. Boudreau has pushed the Capitals to play more aggressively, to forecheck tougher and create scoring chances to spark the once-dormant offense.
Washington has improved to 16-19-5 and is back in the hunt for the playoffs.
"I think they're starting to believe a little bit in themselves, which is really good," Boudreau said. "You look, not necessarily at our record, but at the fact that (when) other teams are scoring first we don't hang our heads, we just say ... we're going to score two or three."
The Capitals pressured Ottawa throughout Saturday's game and did the same thing in the first period of this one. Washington made 15 of its 26 shots in the first period and created numerous scoring chances.
"We knew from the last game we played them that they don't give up," Green said. "Learning from the last game, don't change the way we're playing is the biggest thing. We weren't going to let them step up and take that play again."
Viktor Kozlov scored the other first-period goal. Gordon sealed the victory with an empty-net goal in the third period.
Washington's Alexander Ovechkin added two assists. Kolzig recovered from a shaky start to finish with 31 saves.
Ottawa (25-10-4) scored twice in the game's first five minutes, but Washington took command with five consecutive goals over a 15:37 stretch.
Neil gave Ottawa a 1-0 lead on a breakaway 1:54 into the game. McAmmond made it 2-0 at 4:46 before the Washington offense awakened.
The Capitals got goals from Kozlov, Nylander and Green in a stretch of 2:19 to take a 3-2 lead just 7:34 into the game. Green's goal came 35 seconds after Nylander scored and ended Ottawa goalie Martin Gerber's day.
Gerber allowed three goals on just eight shots. He has allowed 10 goals on just 37 shots against the Capitals this season.
Washington stretched the lead to 4-2 when Laich beat goalie Ray Emery on a back-hander from his knees with 4:15 left in the first period. Green scored on a power-play goal in the first minute of the second period to put the Capitals up 5-2.
"You can tell they feel confident playing us," Ottawa captain Daniel Alfredsson said. "I mean, you see them playing tonight, you'd think they would be at the top of the standings."
- Kozlov's goal was his first since Nov. 8, ending a 23-game dry spell.
- Washington's Alexander Semin (tailbone) and Tom Poti (upper body injury) both missed big parts of this game and are listed day-to-day.
- Ottawa's Jason Spezza's 10-game point-scoring streak ended.